Question

Based on concerns raised by his preliminary research, the biologist decides to collect and examine 150 frogs.

a) Assuming the frequency of the trait is still 1 in 8, determine the mean and standard deviation of the number of frogs with the trait he should expect to find in his sample.
b) Verify that he can use a Normal model to approximate the distribution of the number of frogs with the trait.
c) He found the trait in 22 of his frogs. Do you think this proves that the trait has become more common?
Explain.

Answer 1

Answered and explained below

Explanation:

A) We are told that frequency of the trait is still 1 in 8. Thus, population proportion; p = 1/8 = 0.125

Sample size; n = 150

Formula for mean is;

μ = np

μ = 150 × 0.125

μ = 18.75

Formula for standard deviation is;

σ = √(np(1 - p))

σ = √(150 × 0.125(1 - 0.125))

σ = √16.40625

σ = 4.05

B) usually, when np ≥ 10 , we make use of normal distribution.

I'm this case, it is 18.75 which is greater than 10.

Thus,we can use a normal model to approximate the distribution.

C) we are told that he found the trait in 22 of the frogs.

Thus;

Proportion is now; 22/150 = 0.1467

This is a higher probability that the initial one of 0.125 and we can say that the trait has become more common.