Question

PART1

A. A particular fruit's weights are normally distributed, with a mean of 672 grams and a standard deviation of 38 grams.If you pick 8 fruits at random, then 12% of the time, their mean weight will be greater than how many grams? Give your answer to the nearest gram.

B. On the distant planet Cowabunga , the weights of cows have a normal distribution with a mean of 342 pounds and a standard deviation of 57 pounds. The cow transport truck holds 14 cows and can hold a maximum weight of 5054. If 14 cows are randomly selected from the very large herd to go on the truck, what is the probability their total weight will be over the maximum allowed of 5054? (This is the same as asking what is the probability that their mean weight is over 361.)

C. A manufacturer knows that their items have a normally distributed lifespan, with a mean of 6.8 years, and standard deviation of 0.6 years. If 10 items are picked at random, 7% of the time their mean life will be less than how many years? Give your answer to one decimal place.

D. A manufacturer knows that their items have a normally distributed lifespan, with a mean of 11.6 years, and standard deviation of 1.5 years. If you randomly purchase 8 items, what is the probability that their mean life will be longer than 11 years?

E. A particular fruit's weights are normally distributed, with a mean of 769 grams and a standard deviation of 14 grams. If you pick 19 fruit at random, what is the probability that their mean weight will be between 762 grams and 769 grams

F. A manufacturer knows that their items have a normally distributed length, with a mean of 8.8 inches, and standard deviation of 1.5 inches. If 3 items are chosen at random, what is the probability that their mean length is less than 10.7 inches?

Answer 1