The second-leading genetic cause of mental retardation is Fragile X Syndrome, named for the frag

step 1 Hello everyone, this is problem 93. We will use the person approximation to the binomial distrib

The second-leading genetic cause of mental retardation is...

The second-leading genetic cause of mental retardation is Fragile $\mathrm{X}$ Syndrome, named for the fragile appearance of the tip of the X chromosome in affected individuals. One in 1500 males are 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.

The second-leading genetic cause of mental retardation is Fragile $\mathrm{X}$ Syndrome, named for the fragile appearance of the tip of the X chromosome in affected individuals. One in 1500 males are 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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Key Concepts

Poisson Distribution

The Poisson distribution models the number of events occurring within a fixed interval of time or space, under the assumption that these events occur with a known constant rate and independently. It is characterized by a single parameter ? (lambda), which represents the mean number of occurrences.

Poisson Approximation to the Binomial

The Poisson approximation is a method used to simplify calculations when dealing with a binomial distribution with a large number of trials and a small probability of success. In such cases, the binomial distribution can be approximated by a Poisson distribution where the mean ? is equal to the product of the number of trials and the probability of success.

Binomial Distribution

The binomial distribution describes the number of successes in a fixed number of independent trials, where each trial has the same probability of a success. In this context, each individual male represents a trial, and the number of affected males corresponds to the number of successes.

Expected Value

The expected value in a binomial distribution is calculated as the product of the number of trials and the probability of success. It provides the mean or average number of successes (or affected individuals) that one would expect in a given sample.

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