A population of values has a normal distribution with μ = 155.4 and σ = 49.5 . You intend to draw a random sample of size n = 246 . Find the probability that a single randomly selected value is between 158.6 and 159.2. P(158.6 < X < 159.2) = .0048 Correct Find the probability that a sample of size n = 246 is randomly selected with a mean between 158.6 and 159.2. P(158.6 < M < 159.2) = .0410 Correct

(a) The probability that a single randomly selected value lies between 158.6 and 159.2 is 0.004.

(b) The probability that a sample mean is between 158.6 and 159.2 is 0.0411.

Step-by-step explanation:

Let the random variable X follow a Normal distribution with parameters μ = 155.4 and σ = 49.5.

(a)

Compute the probability that a single randomly selected value lies between 158.6 and 159.2 as follows:

*Use a standard normal table.

Thus, the probability that a single randomly selected value lies between 158.6 and 159.2 is 0.004.

(b)

A sample of n = 246 is selected.

Compute the probability that a sample mean is between 158.6 and 159.2 as follows:

*Use a standard normal table.

Thus, the probability that a sample mean is between 158.6 and 159.2 is 0.0411.