Question

Assume that the random variable X is normally distributed with a population mean of 110 and a population standard deviation of 20.

Compute the probability P(X ≥ 126).

Answer 1

To calculate the probability P(X ≥ 126) in a normal distribution with mean 110 and standard deviation 20, we find the z-score for x = 126 and then calculate the area under the curve to the right of the z-score.

Step-by-step explanation:

To calculate the probability P(X ≥ 126), we need to find the area to the right of x = 126 under the normal distribution curve with a mean of 110 and a standard deviation of 20. Since the z-score formula is given by z = (x - μ)/σ, we first calculate the z-score for x = 126:

z = (126 - 110)/20 = 0.8

Next, we look up the z-score of 0.8 in the standard normal distribution table or use a calculator or software to find the area under the curve to the right of z = 0.8, which is approximately 0.2119.

Therefore, the probability P(X ≥ 126) is approximately 0.2119 or 21.19%.