Reference no: EM132846921
SAMPLING DISTRIBUTIONS
1. Given a normal population whose mean is 50 and whose standard deviation is 5.
a. Find the probability that a random sample of 4 has a mean between 49 and 52.
b. Find the probability that a random sample of 16 has a mean between 49 and 52.
c. Find the probability that a random sample of 25 has a mean between 49 and 52.
2. The heights of North American women are normally distributed with a mean of 64 inches and a standard deviation of 2 inches.
a. What is the probability that a randomly selected woman is taller than 66 inches?
b. A random sample of four women is selected. What is the probability that the sample mean is greater than 66 inches?
c. What is the probability that the mean height of a random sample of 100 women in greater than 66 inches?
3. An automatic machine in a manufacturing process is operating properly if the lengths of an important subcomponent are normally distributed with mean = 117 cm and standard deviation = 5.2 cm.
a. Find the probability that one selected subcomponent is longer than 120 cm.
b. Find the probability that, if four subcomponents are randomly selected, their mean length exceeds 120 cm.
c. Find the probability that if four subcomponents are randomly selected, all four have lengths that exceed 120 cm.
d. The amount of time spent by North American adults watching television per day is normally distributed with a mean of 6 hours and a standard deviation of 1.5 hours.
a. What is the probability that a randomly selected North American adult watches television for more than 7 hours per day?
b. What is the probability that the average time watching television by a random sample of five North American adults is more than 7 hours?
c. What is the probability, that in a random sample of five North American adults, all five watch television for more than 7 hours per day?
5. The manufacturer of cans of salmon, that are supposed to have a net weight of 6 ounces, tells you that the net weight is actually a normal random variable with a mean of 6.05 ounces and a standard deviation of .18 ounce. Suppose you draw a random sample of 36 cans.
a. Find the probability that the mean weight of the sample is less than 5.97 ounces.
b. Suppose your random sample of 36 cans of salmon produced a mean weight of less than 5.97 ounces. Comment on the statement made by the manufacturer.
6. The restaurant in a large commercial building provides coffee for the building's occupants. The restaurateur has determined that the mean number of cups of coffee consumed per day by all the occupants is 2.0 with a standard deviation of 0.6. A new tenant of the building intends to have a total of 125 new employees. What is the probability that the new employees will consume more than 240 cups per day?
7. The assembly line that produces an electronic component of a missile system has historically resulted in a 2% defective rate. A random sample of 800 components is drawn. What is the probability that the defective rate is greater than 4%? Suppose that in the actual random sample drawn the defective rate is 4%. What does that suggest about the defective rate on the assembly line?
8. A university bookstore claims that 50% of its customers are satisfied with the service and their prices.
a. If this claim is true, what is the probability that in a random sample of 600 customers, less than 45% are satisfied?
b. Suppose that in a random sample of 600 customers, 270 express satisfaction with the bookstore. What does this tell you about the bookstore's claim?