Fragile X Syndrome. The second-leading genetic cause of mental retardation is Fragile X Syndrome, named for the fragile appearance of the tip of the X chromosome in affected individuals. One in 1500 males is affected worldwide, with no ethnic bias.a. In a sample of 10,000 males, how many would you expect to have Fragile X Syndrome?b. For a sample of 10,000 males, use the Poisson approximation to the binomial distribution to determine the probability that more than 7 of the males have Fragile X Syndrome; that at most 10 of the males have Fragile X Syndrome.

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Asked Jan 17, 2020
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Fragile X Syndrome. The second-leading genetic cause of mental retardation is Fragile X Syndrome, named for the fragile appearance of the tip of the X chromosome in affected individuals. One in 1500 males is affected worldwide, with no ethnic bias.

a. In a sample of 10,000 males, how many would you expect to have Fragile X Syndrome?
b. For a sample of 10,000 males, use the Poisson approximation to the binomial distribution to determine the probability that more than 7 of the males have Fragile X Syndrome; that at most 10 of the males have Fragile X Syndrome.

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Expert Answer

Step 1

a.

From the given information, 1,500 males is affected worldwide, with no ethnic bias.

The Poisson distribution is approximate binomial probabilities when n is large and p is small. That is n ≥100 and np ≤ 10. Here, n = 10,000 (≥ 100) and p = 1/1500 = 0.00067

The expected number of males have a Fragile X Syndrome can be obtained below:

Statistics homework question answer, step 1, image 1
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Step 2

Thus, the expected number of males have a Fragile X Syndrome is 6.667.

b.

The probability that more than 7 of the males have fragile syndrome is obtained below:

Statistics homework question answer, step 2, image 1
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Step 3

The probability that more than 7 of the males have fragile syndrome is 0.3523.

The probability...

Statistics homework question answer, step 3, image 1
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