High School

Suppose that the weight, \( x \), in pounds, of a 40-year-old man is a normal random variable with mean 147 and standard deviation 16. Calculate \( P(x < 185) \). Round your answer to four decimal places.

Answer :

The probability P(X < 185) is approximately 0.9916.

To calculate the probability P(X < 185) for a normal random variable with mean 147 and standard deviation 16, we need to use the standard normal distribution table or calculator.

First, we need to find the z-score for x = 185:

z = (X - μ) / σ

z = (185 - 147) / 16

z = 38 / 16

z = 2.375

Next, we find the corresponding probability from the standard normal distribution table or calculator:

P(Z < 2.375) ≈ 0.9916

Therefore, the probability P(X < 185) is approximately 0.9916 (rounded to four decimal places).

You can learn more about probability at

https://brainly.com/question/13604758

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