1. Probability Practice 6.2

a) A manufacturer knows that their items have a normally distributed length, with a mean of 14 inches, and standard deviation of 3.9 inches.

If 18 items are chosen at random, what is the probability that their mean length is less than 15 inches?

b) A manufacturer knows that their items have a normally distributed lifespan, with a mean of 7.6 years, and standard deviation of 0.7 years.

If you randomly purchase 13 items, what is the probability that their mean life will be longer than 8 years?

c) A particular fruit's weights are normally distributed, with a mean of 558 grams and a standard deviation of 17 grams.

If you pick 17 fruit at random, what is the probability that their mean weight will be between 551 grams and 560 grams