Question

In: Statistics and Probability

1a. A mail-order computer business has six telephone lines. Let X denote the number of lines...

1a. A mail-order computer business has six telephone lines. Let X denote the number of lines in use at a specified time. Suppose the pmf of X is as given in the accompanying table.

x 0 1 2 3 4 5 6

p(x) 0.12 0.15 0.18 0.25 0.20 0.06 0.04

Calculate the cdf F(x).

x 0 1 2 3 4 5 6

F(x)

- Graph the cdf F(x).

Use the graph to calculate the probabilities of the events given below.

(a) {at most three lines are in use}

(b) {fewer than three lines are in use}

(c) {at least three lines are in use}

(d) {between two and five lines, inclusive, are in use}

2b. A department store sells sport shirts in three sizes (small, medium, and large), three patterns (plaid, print, and stripe), and two sleeve lengths (long and short). The accompanying tables give the proportions of shirts sold in the various category combinations.

Short-sleeved

Pattern

Size Pl Pr St

S 0.04 0.02 0.05

M 0.08 0.05 0.12

L 0.03 0.07 0.08

Long-sleeved

Pattern

Size Pl Pr St

S 0.03 0.02 0.03

M 0.06 0.11 0.07

L 0.04 0.02 0.08

(a) What is the probability that the next shirt sold is a medium, long-sleeved, print shirt?

(b) What is the probability that the next shirt sold is a medium print shirt?

(c) What is the probability that the next shirt sold is a short-sleeved shirt? A long-sleeved shirt?

short-sleeved shirt

long-sleeved shirt

(d) What is the probability that the size of the next shirt sold is medium?

What is the probability that the pattern of the next shirt sold is a print?

(e) Given that the shirt just sold was a short-sleeved plaid, what is the probability that its size was medium? (Round your answer to three decimal places.)

(f) Given that the shirt just sold was a medium plaid, what is the probability that it was short-sleeved? Long-sleeved? (Round your answer to three decimal places.)

short-sleeved

long-sleeved

Expert Solution

orchestra answered 2 years ago

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