Question

In a restaurant, the proportion of people who order coffee with their dinner is .9. A simple random sample of 144 patrons of the restaurant is taken. Round all probabilities to four decimal places.

What is the probability that the proportion of people who will order coffee with their meal is between 0.85 and 0.95?

What is the probability that the proportion of people who will order coffee with their meal is less than .85?

Answer 1

Solution

Given that,

p = 0.9

1 - p = 1 - 0.9 = 0.1

n = 144

= p = 0.9

=  p ( 1 - p ) / n

=   (0.9 * 0.1 / 144) / = 0.025

= 0.025

(a)

P(0.85 < < 0.95)

= P( (0.85 - 0.9) / 0.025 < ( - ) / < (0.95 - 0.9) / 0.025)

= P(-2 < z < 2)

= P(z < 2) - P(z < -2)

= 0.9772 - 0.0228

= 0.9544

Probability = 0.9544

(b)

P( < 0.85) =

= P(( - ) / < (0.85 - 0.9) / 0.025)

= P(z < -2)

= 0.0228

Probability = 0.0228