davenport stat500 week 4 quiz ch 6 and 7

If selecting samples of size n = 10 from a
population with a known mean and standard
deviation, what requirement, if any, must be satisfied in order to assume
that the
distribution of the sample means is a normal distribution?

If z is a standard normal variable, find the
probability.

The probability that z lies between 0.7 and 1.98.

For a standard normal distribution, find the
percentage of data that are more than 1
standard deviation away from the mean.

Solve the problem. Round to the nearest tenth
unless indicated otherwise.

Scores on an English test are normally distributed with a mean of 33.8 and a
standard
deviation of 8.5. Find the score that separates the top 59% from the bottom
41%.

The diameters of bolts produced by a certain
machine are normally distributed with a mean of 0.30 inches and a standard
deviation of 0.01 inches. What percentage of bolts will
have a diameter greater than 0.32 inches?

In one region, the September consumption levels
for single-family homes are found to be
normally distributed with a mean of 1050 kWh and a standard deviation of 218
kWh. If 50
different homes are randomly selected, find the probability that their mean
energy
consumption level for September is greater than 1075 kWh.

True of False.

The central limit theorem states that as the sample size increases, the
distribution of sample means approaches a skewed distribution.

Solve the problem.

The following confidence interval is obtained for a population proportion, p:
0.883<p<0.911. Use these confidence interval limits to find the margin
of error, E.

Use the confidence level and sample data to find
a confidence interval for estimating the population ?. Round your answer to
the same number of decimal places as the sample mean.

Test scores: n = 105; mean x = 70.5; ? = 6.8; 99% confidence

True of False.

If, under a given assumption, the probability of a particular observed event
is exceptionally small (such as less than 0.05), we conclude that the
assumption is probably not correct.

Use the given data to find the minimum sample
size required to estimate the population proportion.

Margin of error: 0.003, confidence level: 94%, p and q unknown

Use the given information to find the minimum
sample size required to estimate an unknown population mean ?.

How many business students must be randomly selected to estimate the mean
monthly earnings of business students at one college? We want 95% confidence
that the sample mean is within $129 of the population mean, and the
population standard deviation is known to be $595.