Question

According to the International Data Corporation, HP is the leading company in the United States in PC sales with about 26% of the market share. Suppose a business researcher randomly selects 130 recent purchasers of PCs in the United States. (Round the value of ? to 2 decimal places. Round the values of z to 2 decimal places. Round your answers to 4 decimal places.)

(a) What is the probability that more than 37 PC purchasers bought an HP computer?

(b) What is the probability that between 27 and 37 PC purchasers (inclusive) bought an HP computer?

(c) What is the probability that fewer than 22 PC purchasers bought an HP computer?

(d) What is the probability that exactly 29 PC purchasers bought an HP computer?

Answer 1

The distribution here is a binomial distribution given as:

This is approximated to a normal distribution as:

a) The probability that more than 37 PC purchasers bought an HP computer is computed as:

P(X > 37 )

Converting this to a standard normal variable, we get:

Getting this from the standard normal tables, we get:

Therefore 0.2611 is the required probability here.

b) The required probability here is computed as:

Applying the continuity correction, we get:

Converting this to a standard normal variable, we get:

Getting this from the standard normal tables, we get:

Therefore 0.6982 is the required probability here.

c) The probability here is computed as:

P(X < 22)

Converting this to a standard normal variable, we get:

Getting this from the standard normal tables, we get:

Therefore 0.0092 is the required probability here.

d) This is computed using the exact binomial probability function as:

Therefore 0.0521 is the required probability here.