Question

According to a recent Catalyst Census, 16% of executive officers were women with companies that have company headquarters in the Midwest. A random sample of 154 executive officers from these companies was selected. What is the probability that more than 20% of this sample is comprised of female employees?

Answer 1

Answer: 0.0885

Step-by-step explanation:

Given : According to a recent Catalyst Census, 16% of executive officers were women with companies that have company headquarters in the Midwest.

i.e. p= 0.16

Sample size : n= 154

Now, the  probability that more than 20% of this sample is comprised of female employees is given by :-

$P(p>0.20)=P(z>\dfrac{0.20-0.16}{\sqrt{\dfrac{0.16(1-0.16)}{154}}})$

[∵ $z=\frac{\hat{p}-p}{\sqrt{\frac{p(1-p)}{n}}}$]

$=P(z>1.35)\approx1-P(z\leq1.35)=1-0.9115=0.0885$  [Using the standard z-value table]

Hence, the required probability = 0.0885