Question

The proportion of Canadians with green eyes is 0.24. As part of a study of the genetic basis for skin sensitivity to sunlight, a research term collects a simple random sample of 500 Canadians. Answer the following questions to 4 places past the decimal.

a) How many people in the sample would you expect to have green eyes?

b) What is the standard deviation of the sample proportion? (Use the normal approximation from now on).

c) What is the probability that the sample proportion will exceed 0.2591?

Answer 1

a)

Expected value = n * p = 500 * 0.24 = 120

b)

Standard deviation = sqrt [ p ( 1 - p) / n ]

= sqrt [ 0.24 ( 1 - 0.24) / 500]

= 0.0191

c)

Using normal approximation,

P( < p ) = P(Z < ( - p) / SD )

So,

P( > 0.2591) = P(Z > ( 0.2591 - 0.24) / 0.0191)

= P(Z > 1)

= 1 - P(Z < 1)

= 1 - 0.8413 (From Z table)

= 0.1587