Question

An institute reported that 60​% of its members indicate that lack of ethical culture within financial firms has contributed most to the lack of trust in the financial industry. Suppose that you select a sample of 100 institute members.

What is the probability that the sample percentage indicating that lack of ethical culture within financial firms has contributed the most to the lack of trust in the financial industry will be between 59​% and 69​%? Please round to four decimals.

Answer 1

Solution :

Given that ,

p = 0.60

1 - p = 0.40

n = 100

= p = 0.60  

= (p*(1-p))/n =  (0.60*0.40) / 100 = 0.04899

P(0.59 < < 0.69 ) = P((0.59 - 0.60)/0.04899 ) < ( - ) /  < (0.69 - 0.60) /0.04899 ) )

= P(-0.20 < z < 1.84 )

= P(z < 1.84) - P(z < -0.20)

= 0.9671 - 0.4207 Using z-table,

= 0.5464

Probability = 0.5464