Question

39. A sample of 375 observations will be taken from an infinite population. The population proportion is equal to 0.85. What is the probability that the sample proportion will be between .81 and .87?

                a. 0.8466

                b. 0.0149

                c. 0.8615

                d. 0.9582

Answer 1

Solution :

Given that ,

p = 0.85

1 - p = 0.15

n = 375

= p = 0.85  

= (p*(1-p))/n =  (0.85*0.15)/ 375= 0.01844

P(0.81 < <0.87 ) = P((0.81-0.85)/0.01844 ) < ( - ) /  < (0.87-0.85) /0.01844 ) )

= P(-2.169 < z < 1.085)

= P(z < 1.085) - P(z < -2.169)

Using standard normal table,

= 0.8466

Probability = 0.8466

Option a is correct.