Question

The proportion of Canadians with green eyes is 0.3. As part of a study of the genetic basis for skin sensitivity to sunlight, a research term collects a simple random sample of 450 Canadians. Answer the following questions to 4 places past the decimal

1. What is the standard deviation of the sample proportion? (Use the normal approximation from now on) (9.72 is incorrect as an answer)

2. What is the probability that the sample proportion will exceed 0.3216?

Answer 1

Solution

Given that,

p = 0.3

1 - p = 1 - 0.3 = 0.7

n = 450

= p = 0.3

1) =  [p( 1 - p ) / n] = [(0.3 * 0.7) / 450 ] = 0.0216

2) P( > 0.3216) = 1 - P( < 0.3216)

= 1 - P(( - ) / < (0.3216 - 0.3) / 0.0216)

= 1 - P(z < 1.00)

Using z table

= 1 - 0.8413

= 0.1587