A company uses parts made in Canada. Delivery from the Canadian supplier is not

Question

A company uses parts made in Canada. Delivery from the Canadian supplier is not constant.    Below is the relative frequency distribution for the number of days between placement of an order and receipt of the order (x).

x

2

3

4

5

6

P(x)

0.150

0.450

0.300

0.075

0.025

a. Find the expected number of days between placing an order and receiving it.

b. Find the standard deviation for days awaiting receipt after placing an order.

c. What is the probability of the wait time is one standard deviation or more away from the expected wait time?

x

2

3

4

5

6

P(x)

0.150

0.450

0.300

0.075

0.025

Explanation / Answer

a. Expected number of days E(X) = x P(x) = 2*0.150 + 3*0.450 + 4*0.300 + 5*0.075 + 6*0.025

= 3.375.

b. Variance V(X) = x2 P(x) - Mean2 = 4*0.150 + 9*0.450 + 16*0.300 + 25*0.075 + 36*0.025 - 3.375*3.375

= 0.834375.

Standard deviation = 0.834375 = 0.9134.

c. Z >= 1

Probability from z table = 0.1587.

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