In: Statistics and Probability
(Round the final answer to 4 decimal digits) 1. A brand name has a 70% recognition rate. Assume the owner f the brand wants to verify that rate by begging with a small sample of 6 randomly select consumers. a. What is the probability that exactly 4 of the selected consumers recognize the brand name?
b. What is the probability that all of the selected consumers recognize the brand name?
c. What is the probability that at least 5 of the selected consumers recognize the brand name?
d. What is the probability that at most 2 of the selected consumers recognize the brand name?
2) . The lengths of pregnancies are normally distributed with a mean of 272 days and a standard deviation of 15 days. If 35 women are randomly selected, find the probability that they have a mean pregnancy between 271 days and 275 days.
3) The body temperatures of adults are normally distributed with a mean of 98.6° F and a standard deviation of 0.50° F. If 25 adults are randomly selected, find the probability that their mean body temperature is greater than 98.4° F.
4) The average number of pounds of red meat a person consumes each year is 190 with a standard deviation of 24 pounds (Source: American Dietetic Association). If a sample of 60 individuals is randomly selected, find the probability that the mean of the sample will be Less than 192 pounds.