Question

The amount of time that a 4th grader reads comic books in a week is normally distributed with a mean of 6 hours and a standard deviation of 2 hours. Suppose a 4th grader is considered addicted if he/she reads comic books for more than 11 hours a week. If twenty 4th graders are to be chosen at random, find the probability that at least one of them is addicted to comic books (round off to second decimal place).

Answer 1

Answer:

The probability that at least one of the 20 4th graders is addicted to comic books is 0.12.

Step-by-step explanation:

Let X = number of hours a 4th grader reads comics and Y = number of 4th grader addicted to reading comics.

The random variable X is continuous and follows a normal distribution with mean, μ = 6 hours and standard deviation, σ = 2 hours.

And the random variable Y is discrete and follows a binomial distribution with success defined as a 4th grader is addicted to reading comics.

Compute the probability that a 4th grader is addicted to reading comics as follows, i.e. determine the value of P (X > 11) .

$P(X>11) = P(\frac{X-\mu}{\sigma} >\frac{11-6}{2})\\=P(Z >2.5)\\=1-P(Z$

Use the Z-table for the probability value.

Now compute the probability that out of 20 fourth graders at least 1 is addicted to comics as follows:

The Binomial probability function is:

$P(Y)=^{n}C_{y} p^{y} (1-p)^{n-y}$

Compute the value of $P(Y\geq 1)$ as follows:

$P(Y\geq 1)=1-P(Y$

Thus, the probability that at least one of the 20 4th graders is addicted to comic books is 0.12.