Question

Seventeen percent of respondents said they bought more funds.

(a) Find the mean and standard deviation of the number of respondents who bought more fund, if groups of 900 fund owners were polled.

(b) In one of these polls of 900 fund owners, 140 respondents bought more mutual fund. Is this unusual?

(Unusual values are either less that μ - 2σ or greater than μ + 2σ).

Answer 1

Solution

Given that,

p = 0.17

1 - p = 1 - 0.17 = 0.83

a) n = 900

= p = 0.17

=  [p( 1 - p ) / n] = [(0.17 * 0.83) / 900 ] = 0.0125

b)    = 0.16

Using z-score formula,

z = -   /   

z = 0.16 - 0.17 / 0.0125

z = -0.80

Is this not unusual, because z-score -0.80 is between -2.00 and 2.00.