High School

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

Answer :

Final answer:

Calculate the probability of a 40-year-old man weighing less than 185 pounds given a mean weight of 147 pounds and standard deviation of 16 pounds.

Explanation:

Given: Mean weight (μ) = 147 pounds, Standard deviation (σ) = 16 pounds

To find: P(x < 185)

Calculation:

  1. Calculate the z-score: z = (185 - 147) / 16 = 2.375
  2. Look up the z-score in the z-table: P(z < 2.375) = 0.9916

Answer: P(x < 185) = 0.9916

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