The scores of students on the SAT college entrance examinations at a certain high school had a normal distribution with mean and standard deviation . (If necessary, round answers below to at least four decimal places.)

(a) What is the probability that a single student randomly chosen from all those taking the test scores 541 or higher?

The probability that a single student randomly chosen from all those taking the test scores 541 or higher is 0.4052.

Step-by-step explanation:

Let us consider a random variable, , then , is a standard normal variate with mean, E (Z) = 0 and Var (Z) = 1. That is, .

The random variable X is defined as the scores of students on the SAT college entrance examinations at a certain high school.

The mean of the scores was, μ = 534.6 and standard deviation of the scores was, σ = 28.2.

The random variable X follows a Normal distribution.

Compute the probability that a single student randomly chosen from all those taking the test scores 541 or higher as follows:

Apply continuity correction:

P (X ≥ 541) = P (X > 541 + 0.50)

                 = P (X > 541.50)

*Use a z-table.

Thus, the probability that a single student randomly chosen from all those taking the test scores 541 or higher is 0.4052.

11 feet 6 inches and 8 feet 6 inches

boxplot e is the answer