 # Statistics Questions

Subject Mathematics General Statistics

## Question

* Find the indicated value
z0.05

* Find the indicated probability.

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?

Assume that the weights of quarters are normally distributed with a mean of 5.67 g and a standard deviation 0.070 g. A vending machine will only accept coins weighing between 5.48 g and 5.82 g. What percentage of legal quarters will be rejected?

* Solve the problem.

Scores on a test have a mean of 70 and Q3 is 84. The scores have a distribution that is approximately normal. Find P90. (You will need to first find the standard deviation.)

* SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Provide an appropriate response.

Personal phone calls received in the last three days by a new employee were 1, 2, and 6. Assume that samples of size 2 are randomly selected with replacement from this population of three values. Identify the probability of each sample, and describe the sampling distribution of the sample means.

The amount of snowfall falling in a certain mountain range is normally distributed with a mean of 80 inches, and a standard deviation of 16 inches. What is the probability that the mean annual snowfall during 64 randomly picked years will exceed 82.8 inches?

* SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.

Under what three conditions is it appropriate to use the t distribution in place of the standard normal distribution?

* Solve the problem. Round the point estimate to the nearest thousandth

Find the point estimate of the proportion of people who wear hearing aids if, in a random sample of 421 people, 40 people had hearing aids.

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.

When 283 college students are randomly selected and surveyed, it is found that 111 own a car. Find a 99% confidence interval for the true proportion of all college students who own a car.

* Solve the problem

A newspaper article about the results of a poll states: "In theory, the results of such a poll, in 99 cases out of 100 should differ by no more than 3 percentage points in either direction from what would have been obtained by interviewing all voters in the United States." Find
the sample size suggested by this statement.

* Do one of the following, as appropriate:
(a) Find the critical value zα/2,
(b) find the critical value tα/2,
(c) state that neither the normal nor the t distribution applies.

90%; n = 10; σ is unknown; population appears to be normally distributed.
95%; n = 11; σ is known; population appears to be very skewed.
91%; n = 45; σ is known; population appears to be very skewed.

* Use the given degree of confidence and sample data to construct a confidence interval for the population mean μ. Assume that the population has a normal distribution.

Thirty randomly selected students took the calculus final. If the sample mean was 77 and the standard deviation was 12.2, construct a 99% confidence interval for the mean score of all students.

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

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 \$136 of the population mean, and the population standard deviation is known to be \$501.

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

44 packages are randomly selected from packages received by a parcel service. The sample
has a mean weight of 16.0 pounds and a standard deviation of 3.7 pounds. What is the 95% confidence interval for the true mean weight, μ, of all packages received by the parcel service?

* Use the given degree of confidence and sample data to find a confidence interval for the population standard deviation σ. Assume that the population has a normal distribution. Round the confidence interval limits to the same number of decimal places as the sample standard deviation.

College students' annual earnings: 98% confidence; n = 9, x = \$3978, s = \$888   ( THE X AFTER 9 HAS A MINUS SIGN ON TOP)

* Find the appropriate minimum sample size.

You want to be 95% confident that the sample variance is within 20% of the population variance.

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