1. The distribution of actual weights of 8-oz chocolate bars produced by a certain machine is normal with a mean of 8.1 ounces and a standard deviation of 0.1 ounces. What is the probability that the mean of 9 such chocolate bars will be less than 8.15 ounces?

2. In a large population of adults, IQ scores are normally distributed with a mean 112 and a standard deviation of 20. What is the probability that the mean IQ of 16 adults will be between 105 and 123?

3. The weights of four randomly chosen bags of oranges, each labeled 10 pounds, were 10.2, 10.5, 10.3, and 10.3 pounds. Assume that the distribution of weights is normal. Find a 90% confidence interval for the mean weight of all bags of oranges.

a. 11.735 1.231

b. 10.325 1.458

c. 15.481 2.325

d. None of these answers.

e. 10.735 1.231

f. 10.325 0.148

4. In the United States, the population mean height for 3-year-old boys is 38 inches. Suppose a random sample of 15 non-U.S. 3-year-old boys showed a sample mean of 37.2 inches with a standard deviation of 3 inches. The boys were selected randomly and independently and the population is approximately normally distributed. Determine whether the population mean of non-U.S. boys is significantly different from the U.S. population mean. Use a significance level of 0.05.

Select the appropriate hypothesis.

a. H_0: =38

H_a: 38

b. Ho:=38

Ha:38

c. None of these answers.

d. H_0: =37.2

H_a: 37.2

e. Ho: p =38

Ha:p38

f. Ho:=38

Ha:< 38

5.In the United States, the population mean height for 3-year-old boys is 38 inches. Suppose a random sample of 15 non-U.S. 3-year-old boys showed a sample mean of 37.2 inches with a standard deviation of 3 inches. The boys were selected randomly and independently and the population is approximately normally distributed. Determine whether the population mean of non-U.S. boys is significantly different from the U.S. population mean. Use a significance level of 0.05.

Find the test statistic.

a. None of these answers.

b. p = 0.319

c. z =1.0328

d. z = -1.0328

e. t =-1.0328

f. t = 1.0328

6. In the United States, the population mean height for 3-year-old boys is 38 inches. Suppose a random sample of 15 non-U.S. 3-year-old boys showed a sample mean of 37.2 inches with a standard deviation of 3 inches. The boys were selected randomly and independently and the population is approximately normally distributed. Determine whether the population mean of non-U.S. boys is significantly different from the U.S. population mean. Use a significance level of 0.05.

Find the p-value