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 obtainedA.      Determine the mean of the sampling distribution of p̂B.      Determine the standard deviation of the sampling distribution of p̂C.      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 15B.      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 154.       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?