#1 A binomial experiment is given. Decide whether you can use the normal distribution to approximate the binomial distribution. If you can, find the mean and standard deviation. If you cannot, explain why.A survey of adults found that 65% have used a multivitamin in the past 12 months. You randomly select 50 adults and ask them if they have used a multivitamin in the past 12 months.

#2 A population has a mean =75 and a standard deviation=8.

Find the mean and standard deviation of a sampling distribution of sample means with sample size n=64.

#3 The population mean and standard deviation are given below. Find the required probability and determine whether the given sample mean would be considered unusual.

For a sample of n=65, find the probability of a sample mean being greater than 216 if =215 and =3.6. (Round to four decimal places as needed.)

#4 The heights of fully grown trees of a specific species are normally distributed, with a mean of 68.0 feet and a standard deviation of 7.00 feet. Random samples of size 13 are drawn from the population. Use the central limit theorem to find the mean and standard error of the sampling distribution.

The mean of the sampling distribution is x=

The standard error of the sampling distribution is x=

(Round to two decimal places as needed.)

#5 Use the central limit theorem to find the mean and standard error of the mean of the indicated sampling distribution. Then sketch a graph of the sampling distribution.

The per capita consumption of red meat by people in a country in a recent year was normally distributed, with a mean of 100 pounds and a standard deviation of 37.4 pounds. Random samples of size 15 are drawn from this population and the mean of each sample is determined.

#6 The mean height of women in a country (ages 2029) is 64.1 inches. A random sample of

50 women in this age group is selected.

What is the probability that the mean height for the sample is greater than 65 inches? Assume

=2.99.

#7 A machine used to fill gallon-sized paint cans is regulated so that the amount of paint dispensed has a mean of 128 ounces and a standard deviation of 0.20 ounce. You randomly select 40 cans and carefully measure the contents. The sample mean of the cans is

127.9 ounces. Does the machine need to be reset? Explain your reasoning.

#8 The weights of ice cream cartons are normally distributed with a mean weight of 8 ounces and a standard deviation of 0.4 ounce.

(a) What is the probability that a randomly selected carton has a weight greater than 8.14 ounces?

(b) A sample of 25 cartons is randomly selected. What is the probability that their mean weight is greater than 8.14 ounces?

#9 The mean percent of childhood asthma prevalence in 43 cities is 2.25%. A random sample of 34 of these cities is selected.

What is the probability that the mean childhood asthma prevalence for the sample is greater than 2.6%?

Interpret this probability. Assume that =1.35%.