Question

A golf club company is deciding whether or not to introduce a new club so they are interested in the proportion of golfers who currently use their brand. The company draws a random sample of 150 golfers. Suppose the true proportion of all golfers who use the company’s clubs is 30%. What is the probability that the sample proportion of golfers is less than 0.35?

Answer 1

Solution :

Given that ,

p = 0.30

1 - p = 0.70

n = 150

= p = 0.30

= (p*(1-p))/n =  (0.30*0.70)/ 150= 0.03742

P( <0.35 ) = P(( - ) / < (0.35 - 0.30) / 0.03742)

= P(z < 1.34) using z-table

= 0.9099

The probability that the sample proportion of golfers is less than 0.35 is 0.9099.