Question

Use Binomial Distribution (i believe)

1) Chromosome defect A occurs in only one out of 200 adult males. A random sample of 100 adult males is selected. Let the random variable ? represent the number of males in the sample who have this chromosome defect.

a) What are the mean and standard deviation of the random variable ??

b) What is the estimated probability that we observe 3 or more adult males with this chromosome defect? (calculate with and without continuity correction).

c) What is the exact distribution of ?? Use this to calculate the probability in part (b).

2) Chromosome defect A occurs in only one out of 200 adult males. A random sample of 100 adult males is selected. Let the random variable ? represent the proportion of males in the sample who have this chromosome defect.

a) What are the theoretical mean and standard deviation of ??

b) What is the distribution of sample proportion?

c) Compute the estimated probability that the sample proportion is 3% or more. Compare your results with the results of the previous question.

Answer 1

1)

Here X has binomial distribution with parameters as follows:

n=100 and p = 1/200 = 0.005

a)

Using normal approximation, X has approximately normal distribution with mean and SD as follows:

b)

With continuity correction:

The z-score for X = 3-0.5 = 2.5 is

The  estimated probability that we observe 3 or more adult males with this chromosome defect is

Without continuity correction:

The z-score for X = 3 is

The  estimated probability that we observe 3 or more adult males with this chromosome defect is

c)

Here X has binomial distribution with parameters as follows:

n=100 and p = 1/200 = 0.005

The  estimated probability that we observe 3 or more adult males with this chromosome defect is

Excel function used: "=1-BINOMDIST(2,100,0.005,TRUE)"

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2)

(a-b)

The sampling distribution of sample proportion, U, will be approximately normal with mean

and standard deviation

c)

The z-score for is

The estimated probability that the sample proportion is 3% or more is