In Exercises 53 and 54, find the mean and standard deviation of the indicated sampling distribution of sample means. Then sketch a graph of the sampling distribution.


The population densities in people per square mile in the 50 U.S. states have a mean of 199.6 and a standard deviation of 265.4. Random samples of size 35 are drawn from this population, and the mean of each sample is determined.

In Exercises 69 and 70, determine whether you can use a normal distribution to approximate the binomial distribution. If you can, use the normal distribution to approximate the indicated probabilities and sketch their graphs. If you cannot, explain why and use a binomial distribution to find the indicated probabilities.

A survey of U.S. adults found that 72% used a mobile device to manage their bank account at least once in the previous month. You randomly select 70 U.S. adults and ask whether they used a mobile device to manage their bank account at least once in the previous month. Find the probability that the number who have done so is (c) greater than 60.

In Exercises 55–60, find the indicated probabilities and interpret the results.

The mean annual salary for Level 1 actuaries in the United States is about \$72,000. A random sample of 45 Level 1 actuaries is selected. What is the probability that the mean annual salary of the sample is (b) more than \$68,000? Assume sigma = \$11,000.

In Exercises 51 and 52, a population and sample size are given. (b) List all samples (with replacement) of the given size from the population and find the mean of each. (c) Find the mean and standard deviation of the sampling distribution of sample means and compare them with the mean and standard deviation of the population.

The goals scored in a season by the four starting defenders on a soccer team are 1, 2, 0, and 3. Use a sample size of 2.

In Exercises 69 and 70, determine whether you can use a normal distribution to approximate the binomial distribution. If you can, use the normal distribution to approximate the indicated probabilities and sketch their graphs. If you cannot, explain why and use a binomial distribution to find the indicated probabilities.

A survey of U.S. adults found that 72% used a mobile device to manage their bank account at least once in the previous month. You randomly select 70 U.S. adults and ask whether they used a mobile device to manage their bank account at least once in the previous month. Find the probability that the number who have done so is (a) at most 40.

In Exercises 61 and 62, a binomial experiment is given. Determine whether you can use a normal distribution to approximate the binomial distribution. If you can, find the mean and standard deviation. If you cannot, explain why.

A survey of U.S. adults ages 33 to 40 earning more than \$150,000 per year found that 94% are content with how their lives have turned out so far. You randomly select 20 U.S. adults ages 33 to 40 earning more than \$150,000 and ask if they are content with their lives so far.

In Exercises 69 and 70, determine whether you can use a normal distribution to approximate the binomial distribution. If you can, use the normal distribution to approximate the indicated probabilities and sketch their graphs. If you cannot, explain why and use a binomial distribution to find the indicated probabilities.

A survey of U.S. adults found that 72% used a mobile device to manage their bank account at least once in the previous month. You randomly select 70 U.S. adults and ask whether they used a mobile device to manage their bank account at least once in the previous month. Find the probability that the number who have done so is (b) exactly 50.