Statistics and Probability

Question

Based on historical data, your manager believes that 34% of the company's orders come from first-time customers. A random sample of 109 orders will be used to estimate the proportion of first-time-customers. What is the probability that the sample proportion is between 0.2 and 0.46?

Answer 1

n=109

mean=.34(109)=np- 37.06

var=npq=37.06(.66)=24.4596

s= sqrnpq =sqr(24.4596= about 4.95

4.95/109=

p(.2<x<.46)=about 99.7%

.34-.2=.14

.14/4.95/109=3.4=z1

.4997

.46-.34=.12

.12/4.95/109=2.8=z2

.4974

add the areas

.4997+.4974=.9971

use z tables