Question

Weights (x) of men in a certain age group have a normal distribution with mean μ = 150 pounds and standard deviation σ = 28 pounds. Find each of the following probabilities. (Round all answers to four decimal places.) (a) Find the probability that the weight of a randomly selected man is less than or equal to 185 pounds.

Answer 1

To find the probability that the weight of a randomly selected man is less than or equal to 185 pounds, calculate the z-score and use the standard normal distribution table.

Step-by-step explanation:

To find the probability that the weight of a randomly selected man is less than or equal to 185 pounds, we need to calculate the z-score and then use the standard normal distribution table.

1. Calculate the z-score using the formula: z = (x - μ) / σ, where x = 185 pounds, μ = 150 pounds, and σ = 28 pounds.
2. Using the z-score, find the corresponding probability from the standard normal distribution table.

Let's calculate the z-score:

z = (185 - 150) / 28 = 1.25

Using the z-score of 1.25, we can find the corresponding probability of P(Z ≤ 1.25) from the standard normal distribution table. The table value is 0.8944.

Therefore, the probability that the weight of a randomly selected man is less than or equal to 185 pounds is approximately 0.8944.