a.A manufacturer knows that their items have a normally distributed length, with a mean of 8.4 inches, and standard deviation of 0.8 inches.

If one item is chosen at random, what is the probability that it is less than 7.4 inches long?

b.A population of values has a normal distribution with=144.5and=89.8. You intend to draw a random sample of sizen=100

Find the probability that a sample of sizen=100n=100is randomly selected with a mean between 129.2 and 131.9.

P(129.2 <M< 131.9) =

c.LetXrepresent the full height of a certain species of tree. Assume thatXXhas a normal probability distribution with a mean of 126.4 ft and a standard deviation of 9.1 ft.

A tree of this type grows in my backyard, and it stands 111.8 feet tall. Find the probability that the height of a randomly selected tree is as tall as mine or shorter.

P(X<111.8)=

d.On the distant planet Cowabunga the weights of cows have a normal distribution with a mean of 413 pounds and a standard deviation of 42 pounds. The cow transport truck holds 5 cows and can hold a maximum weight of 2290. If 5 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 2290? (This is the same as asking what is the probability that their mean weight is over 458.)

P(M>458)=

e.LetXrepresent the full height of certain species of tree. Assume thatXis normally distributed with a mean of 88.2 feet and a standard deviation of 56.6 feet.

Find the probability that the full height of a randomly selected tree is greater than 37.3 feet.

P(X>37.3)=