Question

An institute reported that 63% 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 you select a sample off 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 72%?

Answer 1

Solution:

Given that,

n = 100

=0.63

1 - = 1 - 0.63= 0.37

=   = 0.63

= ( 1 - ) / n

=   0.63 * 0.37 / 100

= 0.0483

= 0.0483

P( 0.59 < < 0.72 )  

P( 0.59 - 0.63 / 0.0483 ) < ( -    / ) < ( 0.72 - 0.63 / 0.0483 )

P ( -0.04 /0.0483 < z < 0.09 / 0.0483 )

P ( - 1.05 < z < 1.86 )

P ( z < 1.86 ) - p ( z < -0.83 )

Using z table

= 0.9686 - 0.2033

= 0.7653

Probability = 0.7653 = 76.53%