Question

# An institute reported that 65​% of its members indicate that lack of ethical culture within financial...

An institute reported that

65​%

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. Complete parts ​(a) through ​(d) below.

a. 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

64​%

and

71​%?

Solution

Given that,

p = 0.65

1 - p = 1 -0.65 =0.35

n = 100

= p =0.65

=  [p ( 1 - p ) / n] = [(0.65*0.35) /100 ] = 0.0477

= P(0.64 << 0.71)= P[(0.64 -0.65) /0.0477 < ( - ) / < (0.71 -0.65) /0.0477 ]

= P(-0.31 < z <1.26 )

= P(z < 1.26) - P(z <-0.31 )

Using z table

=0.8962-0.3783

=0.5179

probability= 0.5179

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