Question

calculate:

PART A:   Delivery times for shipments from a central warehouse are exponentially distributed with a mean of 2.63 days (note that times are measured continuously, not just in number of days). A random sample of 143 shipments are selected and their shipping times are observed.
Approximate the probability that the average shipping time is less than 2.29 days.
    Enter your answer as a number accurate to 4 decimal places.

PART B: A manufacturer knows that their items have a normally distributed length, with a mean of 8.1 inches, and standard deviation of 2.5 inches.

If one item is chosen at random, what is the probability that it is less than 9.2 inches long?  (Round to four decimal places.)

PART C:  On the distant planet Cowabunga , the weights of cows have a normal distribution with a mean of 336 pounds and a standard deviation of 41 pounds. The cow transport truck holds 14 cows and can hold a maximum weight of 5026. 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 5026? (This is the same as asking what is the probability that their mean weight is over 359.)

(Give answer correct to at least three decimal places.)
probability =

Answer 1

B)

P(x < 9.2)
= P(z < (9.2 - 8.1)/2.5)
= P(z < 0.44)
= 0.6700

c)

5026/14 = 359

P(x > 359)
= P(z > (359 - 336)/(41/sqrt(14))
= P(z >2.0990)
= 0.018