The weight of a sperm whale’s brain is normally distributed with a mean of 15.5 pounds and a standard deviation of 3.6 pounds.

Question

The weight of a sperm whale’s brain is normally distributed with a mean of 15.5 pounds and a standard deviation of 3.6 pounds. What is the probability a randomly selected sperm whale will have a brain that weighs less than 20 pounds?

 

 

The answer is 0.8944, but I’m not sure how they got that answer. 

Answer 1

To use the standard normal distribution table in your book, you will need to calculate the z-score from the given data.

z = (X - μ)/σ

  = (20 - 15.5)/3.6 = 1.25

 

The probability a randomly selected sperm whale will have a brain that weighs less than 20 pounds is

P{X ≤ 20} = P{z ≤ 1.25}

                = 0.8944