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# Statistics

1. Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with a mean of 207 and a standard deviation of 17 days.

A. What is the probability that a randomly selected pregnancy lasts less than 201 days?

B. What is the probability that a random sample of 16 pregnancies has a mean gestation period of 201 days or less?

C. What is the probability that a random sample of 37 pregnancies has a mean gestation period of 201 days or less?

2. According to a survey in a country, 38% of adults do not have any credit cards. Suppose a simple random sample of 900 adults is obtained

A. Determine the mean of the sampling distribution of p̂

B. Determine the standard deviation of the sampling distribution of p̂

C. In a random sample of 900 adults, what is the probability that less than 36% have no credit cards?

3. A simple random sample of size n is drawn from a population that is normally distributed. The sample mean is found to be 114 and the sample standard deviation is found to be 10.

A. Construct a 90% confidence interval about μ if the sample size n is 15

B. Construct a 90% confidence interval about μ if the sample size n is 21

C. Construct a 99% confidence interval about μ if the sample size n is 15

4. An interactive poll found that 350 of 2393 adults aged 18 or older have at least one tattoo.

A. Obtain a point estimate for the proportion of adults who have at least one tattoo.

B. Construct a 95% confidence interval for the proportion of adults with at least one tattoo.

C. Construct a 98% confidence interval for the proportion of adults with at least one tattoo.

D. What is the effect of increasing the level of confidence on the width of the interval?