Directions: Complete ALL of the following problems.

When necessary, use the following formula:

  1. The National Center for Education Statistics claims in its Digest of Education

Statistics that of all public elementary schools have between 250 and 499 students. For one particular city, the mean number of students per public elementary school is 475 with a standard deviation of 33 students. A random sample of 36 public elementary schools in the city is taken. What is the probability that the mean number of students per school in these schools is less than 465?

  1. Use the population of ages of the three U.S. presidents (Lincoln, Garfield, McKinley) when they were assassinated in office. Assume that random sample of size are selected with replacement.
  1. List the different possible samples along with the probability of each sample, then construct a table representing the sampling distribution of the sample variances.
  1. Compare the variance of to the mean of the sampling distribution of the sample variance.
  1. Do the sample variances target the value of the population variance? In general, do sample variances make good estimators of population variances?

Why or why not?

  1. The U.S. Department of Education reports that the mean number of hours per school week that elementary and high school teachers’ work is 50. If a sample of 40 teachers is randomly selected, what is the probability that the mean numbers of hours these teachers work is at least 55 hours per school week? Assume that the standard deviation is 14 hours.
  1. The mean amount of money that a depositor of the Second National City Bank has in an account is $5000 with a standard deviation of $650. A random sample of 36 accounts is taken. What is the probability that the mean amount of money that these 36 depositors have in their accounts is between $4800 and $5300?
  1. The population is the weight of four pumpkins (in pounds) displayed in a carnival “guess the weight” game booth. Obtain the sampling distribution of the sample mean for a sample size of 2 pumpkins using replacement. Do the sample means target the population mean? Why or why not?

6. The average age at which men in the United States marry for the first time is

24.8 years (Source: Statistical Abstract of the United States, 1994). If 1 of the men is randomly selected, what is the probability that the age at which he married for the first time is at most 25.2 years? (Assume that the standard deviation is

2.7 years). If a sample of 55 married men is randomly selected, what is the probability that they have a mean age at which they marry for the first time is

at most 25.2 years? Given these results, does it seem that this statistical source is correct?