Question

According to the most recent​ data, 12.3​% of engineers​ (electrical, mechanical,​ civil, and​ industrial) were women. Suppose a random sample of 80 engineers is selected. a. How likely is it that a random sample of 80 people will contain 12 or more women in these​ positions? b. How likely is it that the random sample will contain fewer than 5 women in these​ positions? c. If the random sample included 160 ​engineers, how would this change your answer to part​ b?

Answer 1

Explanation:

Given that according to the most recent data, 12.3​% of engineers​ (electrical, mechanical,​ civil, and​ industrial) were women.

n =80

p is normal with p = 12.3% and std error =
`\sqrt{(0.123(0.877)/(80) } =0.03672`

Prob 12 or more women = P(p>0.15)

=P(Z>
`(0.15-0.123)/(0.03672) =0.74)`

=0.5-0.2704=0.2296