Question

Suppose that 12% of all males suffer some form of color blindness.

What is the mean ___ and standard deviation ___ of the sampling disrtibution of the proportion?

Find the probability that in a random sample of 200 men at least 14% will suffer some form of color
blindness. ___

Answer 1

Step-by-step explanation:

The mean and standard deviation are:

μ = p

σ = √(pq/n)

Given p = 0.12, q = 0.88, and n = 200:

μ = 0.12

σ = √(0.12 × 0.88 / 200)

σ = 0.023

Since the sample is large, it can be approximated with a normal distribution.  Find the z-score:

z = (x − μ) / σ

z = (0.14 − 0.12) / 0.023

z = 0.87

Use a calculator or table to find the probability:

P(Z > 0.87) = 1 − 0.8078

P(Z > 0.87) = 0.1922