Question

40% of the employees at a large corporation are female. A sample of 50 employees is taken and
gender is recorded. What is the probability of a sample proportion of females in the sample between
35 and 452?​

Answer 1

Explanation:

The sample proportion will be on average 40% plus/minus a standard error which decreases as the size of the sample gets larger.

x=μ±σn√x=0.4±0.4(1–0.4)√50√x=0.4±0.06928

The distribution of this sample proportion can be approximated with the normal bell curve. To find the probability that x is between 0.35 and 0.45, find the appropriate z score and look up the probability in a standard normal table.

z1=.45−.4.06928=0.72z2=.35−.4.06928=−0.72

P(.35<x<.45)=P(−.72<z<.72)=0.528

The probability that the female sample proportion is between .35 and .45 is about 52.8%

Answer 2

Answer:

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