Question

A recent survey of 2,000 randomly selected U.S. residents asked whether or not they had used the Internet for making travel reservations. There were 1,100 people who answered “yes,” and the remainder answered “no.” Let X be the number of people who answered “yes." Estimate the proportion p from this information. Then calculate the probability that X is less than 1,050.

a. 0.0014

b. 0.5500

c. 0.0131

d. 0.0117

e. 0.9869

Answer 1

Solution:

Given: A recent survey of 2,000 randomly selected U.S. residents asked whether or not they had used the Internet for making travel reservations.

There were 1,100 people who answered “yes,” and the remainder answered “no.”

Part i)

We have to estimate the proportion of the number of people who answered “yes." that is we have to estimate p.

Thus estimate the proportion of the number of people who answered “yes" is

Thus correct option is: b. 0.5500

Part ii)

We have to calculate the probability that X is less than 1,050.

That is:

P( X < 1050)   =.............?

Lets convert this X in proportion.

Now convert in z score .

z score formula is:

Thus we get:

Thus look in z table for z = -2.2 and 0.05 and find corresponding area.

Thus from z table , we get: P( Z < -2.25) =0.0122

Thus