Week 4 forum
Suppose that a class contains 15 boys and 30 girls, and that 10 students are to be selected at random for a special assignment. Find the probability that exactly 3 boys will be selected.
To make a post to this week’s Challenge Discussion Forum, click on the “Counting isn’t always easy” link, then click Post New Thread. In the title block of the dialog box that appears kindly insert your first and last name; compose your post in the message box; and then click Post Message.
Suppose that the percentage annual return you obtain when you invest a dollar in gold or the stock market is dependent on the general state of the national economy as indicated below. For example, the probability that the economy will be in “boom” state is 0.15. In this case, if you invest in the stock market your return is assumed to be 25%; on the other hand if you invest in gold when the economy is in a “boom” state your return will be minus 30%. Likewise for the other possible states of the economy. Note that the sum of the probabilities has to be 1–and is.
State of Economy***Probability***MarketReturn***GoldReturn
Boom****************0.15************25%*************(-30%)
Moderate Growth******0.35************20%***************(-9%)
Weak Growth*********0.25*************5%**************35%
No Growth***********0.25***********(-14%)**************50%
Based on the expected return, would you rather invest your money in the stock market or in gold? Why?
To make a post to this week’s Challenge Discussion Forum, click on the Decision Alternatives link, then click Post New Thread. In the title block of the dialog box that appears kindly insert your first and last name; compose your post in the message box; and then click Post Message.
Suppose that the demand for a company’s product in weeks 1, 2, and 3 are each normally distributed and the mean demand during each of these three weeks is 50, 45, and 65, respectively. Suppose the standard deviation of the demand during each of these three weeks is known to be 10, 5, and 15, respectively. It turns out that if we can assume that these three demands are probabilistically independent then the total demand for the three week period is also normally distributed. And, the mean demand for the entire three week period is the sum of the individual means. Likewise, the variance of the demand for the entire three week period is the sum of the individual weekly variances. But be careful! The standard deviation of the demand for the entire 3 week period is not the sum of the individual standard deviations. Square roots don’t work that way!
Now, suppose that the company currently has 180 units in stock, and it will not be receiving any further shipments from its supplier for at least 3 weeks. What is the probability that the company will run out of units?
To make a post to this week’s Challenge Discussion Forum, click on the Using the Normal Distribution link, then click Post New Thread. In the title block of the dialog box that appears kindly insert your first and last name; compose your post in the message box; and then click Post Message.
Political polls typically sample randomly from the U.S population to investigate the percentage of voters who favor some candidate or issue. The number of people polled is usually on the order of 1000. Suppose that one such poll asks voters how they feel about the President’s handling of the crisis in the financial markets. The results show that 575 out of the 1280 people polled say they either “approve” or “strongly approve” of the President’s handling of this matter. Based on the sample referenced above, find a 95% confidence interval estimate for the proportion of the entire voter population who “approve” or “strongly approve” of the President’s handling of the crisis in the financial markets.
Now, here’s an interesting twist. If the same sample proportion was found in a sample twice as large—that is, 1150 out of 2560—how would this affect the confidence interval?
To make a post to this week’s Challenge Discussion Forum, click on the Build a Confidence Interval Estimate link, then click Post New Thread. In the title block of the dialog box that appears kindly insert your first and last name; compose your post in the message box; and then click Post Message.
A new process for producing synthetic diamonds can be operated at a profitable level only if the average weight of the diamonds produced by the process is greater than 0.5 karat. To evaluate the profitability of the process, a sample of six diamonds was generated using this new process, with recorded weights .46, .61, .52, .48, .57, and .54 karat. Do the six measurements present sufficient evidence to indicate that the average weight of the diamonds produced by the new process is in excess of 0.5 karat? To answer this question conduct an appropriate test of hypothesis using the five step process outlined in our textbook and utilized in the solutions to the Chapter 8 review problems, which are posted in the Review Problem Sets Solutions folder in the Resources section of our classroom.
To make a post to this week’s Challenge Discussion Forum, click on the Testing a Hypothesis link, then click Post New Thread. In the title block of the dialog box that appears kindly insert your first and last name; compose your post in the message box; and then click Post Message.
0.0/ 1.0 Points
For a boxplot, the vertical line inside the box indicates the location of the
A.median
B.mode
In C.mean
D.inter quartile range
Answer Key:
Part 2 of 9 – 2.0/ 2.0 Points
Question 2 of 25
1.0/ 1.0 Points
If events A and B are mutually exclusive, then the probability of both events occurring simultaneously is equal to
A.0.5
B.1.0
C.any value between 0.5 and 1.0
D.0.0
Answer Key:
Question 3 of 25
1.0/ 1.0 Points
If P(A) = P(A|B), then events A and B are said to be
A.complementary
B.mutually exclusive
C.exhaustive
D.independent
Answer Key:
Part 3 of 9 – 3.0/ 3.0 Points
Question 4 of 25
1.0/ 1.0 Points
Suppose that 50 identical batteries are being tested. After 8 hours of continuous use, assume that a given battery is still operating with a probability of 0.70 and has failed with a probability of 0.30.
What is the probability that greater than 40 batteries will last at least 8 hours?
A.0.0789
B.0.4538
C.0.9598
D.0.0402
Answer Key:
Question 5 of 25
1.0/ 1.0 Points
If a gambler rolls two dice and gets a sum of 10, he wins $10, and if he gets a sum of three, he wins $20. The cost to play the game is $5. What is the expectation of this game?
A.$3.06
B.-$2.78
C.-$3.06
D.$2.78
Answer Key:
Question 6 of 25
1.0/ 1.0 Points
There are two types of random variables, they are
A.real and unreal
B.exhaustive and mutually exclusive
C.complementary and cumulative
D.discrete and continuous
Answer Key:
Part 4 of 9 – 5.0/ 6.0 Points
Question 7 of 25
1.0/ 1.0 Points
The theorem that states that the sampling distribution of the sample mean is approximately normal when the sample size n is reasonably large is known as the:
A.simple random sample theorem
B.central tendency theorem
C.point estimate theorem
D.central limit theorem
Answer Key:
Question 8 of 25
1.0/ 1.0 Points
The normal distribution is:
A.a binomial distribution with only one parameter
B.a discrete distribution
C.a density function of a discrete random variable
D.the single most important distribution in statistics
Answer Key:
Question 9 of 25
1.0/ 1.0 Points
If Z is a standard normal random variable, then the value z for which P(-z < Z < z) equals 0.8764 is
A.1.16
B.0.3764
C.1.54
D.3.08
Answer Key:
Question 10 of 25
1.0/ 1.0 Points
Given that Z is a standard normal random variable, P(-1.0 < Z < 1.5) is
A.0.9332
B.0.0919
C.0.7745
D.0.8413
Answer Key:
Question 11 of 25
0.0/ 1.0 Points
One reason for standardizing random variables is to measure variables with:
A.different means and standard deviations on a non-standard scale
B.dissimilar means and similar standard deviations in like terms
In C.similar means and standard deviations on two scales
D.different means and standard deviations on a single scale
Answer Key:
Question 12 of 25
1.0/ 1.0 Points
The standard deviation of a probability distribution is a:
A.measure of variability of the distribution
B.measure of central location
C.measure of skewness of the distribution
D.measure of relative likelihood
Answer Key:
Part 5 of 9 – 1.0/ 1.0 Points
Question 13 of 25
1.0/ 1.0 Points
Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.
Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values.
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.
A sample of 150 students at a State University was taken after the final business statistics exam to ask them whether they went partying the weekend before the final or spent the weekend studying, and whether they did well or poorly on the final. The following table contains the result.
Did Well on Exam Did Poorly on Exam
Studying for Exam 60 15
Went Partying 22 53
If the sample is a good representation of the population, what percentage of the students in the population should we expect to spend the weekend studying and do poorly on the final exam? Place your answer in the blank, rounded to 2 decimal places. Do not use a percentage sign (%). For example, 44.44 would be a legitimate answer. 10.00
Answer Key:
Part 6 of 9 – 2.0/ 2.0 Points
Question 14 of 25
1.0/ 1.0 Points
Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.
Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values.
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.
Find the mean of the distribution shown below.
X 0 1 2
P(X) 0.24 0.31 0.45
Round your answer to two decimal place as necessary. For example, 4.56 would be a legitimate entry.
Mean = 1.21
Answer Key:
Feedback: Expected value = (0)(0.24) + (1)(0.31) + (2)(0.45) = 1.21
Question 15 of 25
1.0/ 1.0 Points
Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.
Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values.
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.
Find the mean of the following probability distribution.
X 1 2 3 4 5
P(X) 0.20 0.10 0.35 0.05 0.30
Round your answer to two decimal place as necessary. For example, 4.56 would be a legitimate entry.
Mean = 3.15
Answer Key:
Part 7 of 9 – 2.0/ 2.0 Points
Question 16 of 25
1.0/ 1.0 Points
Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.
Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values.
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.
At a certain college, there were 600 science majors, 200 engineering majors, and 500 business majors. If a student is selected at random, what is the probability that the student is an engineering major?
Place your answer, rounded to four decimal places, in the blank. 0.1538 When entering your answer do not use any labels or symbols other than a decimal point. Simply provide the numerical value. For example, 0.1234 would be a legitimate entry.
Answer Key: 0
Question 17 of 25
1.0/ 1.0 Points
Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.
Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values.
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.
A reading list for a course contains 20 articles. How many ways are there to choose three articles from this list? Place your answer in the blank. Do not use any decimal places or commas. For example, 45 would be a legitimate entry. 1140
Answer Key:
Part 8 of 9 – 5.0/ 6.0 Points
Question 18 of 25
1.0/ 1.0 Points
Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.
Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values.
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.
Suppose that the average weekly earnings for employees in general automotive repair shops is $450, and that the standard deviation for the weekly earnings for such employees is $50. A sample of 100 such employees is selected at random.
Find the probability that the mean of the sample is between $445 and $455. Place your answer, rounded to 4 decimal places, in the blank. For example, 0.2345 would be a legitimate entry. 0.6826
Answer Key: 0.
Question 19 of 25
1.0/ 1.0 Points
Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.
Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values.
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.
The mean weight of loads of coal placed in train cars by a loading machine is 43.0 tons with a standard deviation of 8.0 tons. Assuming that the weight of loads placed in the train cars by this loader are normally distributed, if a random sample of 9 loads is chosen for a weight check, find the probability that the mean weight of those loads is more than 40.60 tons.
Place your answer, rounded to four decimal places, in the blank. 0.8159 When entering your answer do not use any labels or symbols other than a decimal point. Simply provide the numerical value. For example, 0.1234 would be a legitimate entry.
Answer Key: 0
Question 20 of 25
1.0/ 1.0 Points
Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.
Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values.
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.
Scores on a mathematics examination appear to follow a normal distribution with mean of 65 and standard deviation of 15. The instructor wishes to give a grade of “C” to students scoring between the 60th and 70th percentiles on the exam.
What score represents the 60th percentile score on the mathematics exam? Place your answer in the blank, rounded to a whole number. For example, 62 would be a legitimate entry. 69
Answer Key:
Question 21 of 25
1.0/ 1.0 Points
Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.
Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values.
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.
A Wendy’s fast-food restaurant sells hamburgers and chicken sandwiches. On a typical weekday, the demand for hamburgers is normally distributed with a mean of 450 and standard deviation of 80 and the demand for chicken sandwiches is normally distributed with a mean of 120 and standard deviation of 30.
How many hamburgers must the restaurant stock to be 99% sure of not running out on a given day? Place you answer, rounded to the nearest whole number in the blank. For example, 345 would be a legitimate entry. 637
Answer Key:
Question 22 of 25
0.0/ 1.0 Points
Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.
Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values.
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.
The manufacturer of a new compact car claims the miles per gallon (mpg) for the gasoline consumption is mound shaped and symmetric with a mean of 25.9 mpg and a standard deviation of 9.5 mpg. If 30 such cars are tested, what is the probability the average mpg achieved by these 30 cars will be greater than 28? Place your answer, rounded to 4 decimal places, in the blank. 0.3520
Answer Key: 0.
Question 23 of 25
1.0/ 1.0 Points
Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.
Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values.
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.
A popular retail store knows that the purchase amounts by its customers is a random variable that follows a normal distribution with a mean of $30 and a standard deviation of $9.
What is the probability that a randomly selected customer will spend less than $15 at this store? Place your answer, rounded to 4 decimal places, in the blank. For example, 0.3456 would be a legitimate entry. .0478
Answer Key:
Part 9 of 9 – 1.0/ 2.0 Points
Question 24 of 25
1.0/ 1.0 Points
The sampling distribution of the mean will have the same mean as the original population from which the samples were drawn.
True
False
Answer Key: True
Question 25 of 25
0.0/ 1.0 Points
Using the standard normal curve, the Z- score representing the 5th percentile is 1.645.
In
True
False
Answer Key:
1.0/ 1.0 Points
The total frequency of the data whose ogive is shown below is approximately
A.12
B.18
C.34
D.90
Answer Key:
Question 2 of 20
1.0/ 1.0 Points
The length of the box in the boxplot portrays the
A.median
B.mean
C.interquartile range
D.range
Answer Key:
Question 3 of 20
1.0/ 1.0 Points
Which measure of central location is meaningful when the data are categorical?
A.The mean
B.The mode
C.The median
D.The range
Answer Key:
Question 4 of 20
1.0/ 1.0 Points
Data that arise from counts are called:
A.counted data
B.nominal data
C.discrete data
D.continuous data
Answer Key:
Question 5 of 20
1.0/ 1.0 Points
The median can also be described as:
A.the middle observation when the data values are arranged in ascending orde
B.the second quartile
C.the 50th percentile
D.all of the above
Answer Key:
Question 6 of 20
1.0/ 1.0 Points
A scatterplot allows one to see:
A.whether there is any relationship between two variables
B.what type of relationship there is between two variables
C.Both (a) and (b) are
D.Neither (a) nor (b) is
Answer Key:
Question 7 of 20
0.0/ 1.0 Points
Suppose that a histogram of a data set is approximately symmetric and “bell shaped”. Approximately what percent of the observations are within one standard deviation of the mean?
A.50%
B.68%
C.99.7%
In D.95%
Answer Key:
Question 8 of 20
1.0/ 1.0 Points
Researchers may gain insight into the characteristics of a population by examining a
A.replica
B.sample of the population
C.description of the population
D.mathematical model describing the population
Answer Key:
Question 9 of 20
1.0/ 1.0 Points
The difference between the first and third quartile is called the
A.interquartile range
B.interdependent range
C.mid range
D.unimodal range
Answer Key:
Question 10 of 20
1.0/ 1.0 Points
Boxplots are most useful for.
A.comparing the mean to the median
B.comparing two populations graphically
C.calculating the mean of the data
D.calculating the median of the data
Answer Key:
Question 11 of 20
0.0/ 1.0 Points
Find the z-score for each student and indicate which one has a better relative position. An Art Major earned a grade of 46 on an exam with f$ar{x}f$ = 50 and s = 5; A Theater Major earned a grade of 70 on an exam with f$ar{x}f$ = 75 and s = 7.
A.Both students have the same score.
B.The theater major has a higher relative position than the art major.
C.The higher score cannot be determined.
In D.The art major has a higher relative position than the theater major.
Answer Key:
Question 12 of 20
1.0/ 1.0 Points
What type of graph is the figure below?
A.ogive
B.Pareto chart
C.relative frequency histogram
D.pictograph
Answer Key:
Part 2 of 3 – 4.0/ 6.0 Points
Question 13 of 20
1.0/ 1.0 Points
Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.
Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values.
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.
The following data represent the number of children in a sample of 10 families from Chicago: 4, 2, 1, 1, 5, 3, 0, 1, 0, and 2.
Compute the mean number of children. Place your answer, rounded to two decimal places, in the blank. For example, 3.45 would be a legitimate entry. 1.90
Answer Key:
Question 14 of 20
1.0/ 1.0 Points
Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.
Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values.
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.
A student scored 84 points on a test where the mean score was 79 and the standard deviation was 4. Find the student’s z score, rounded to 2 decimal places, and place it in the blank. 1.25
Answer Key:
Question 15 of 20
1.0/ 1.0 Points
Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.
Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values.
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.
The following data represent the number of children in a sample of 10 families from Chicago: 4, 2, 1, 1, 5, 3, 0, 1, 0, and 2.
Compute the median number of children. Place your answer, rounded to two decimal places, in the blank. For example, 3.45 would be a legitimate entry. 1.50
Answer Key:
Question 16 of 20
1.0/ 1.0 Points
