The length of an adult male killer whale is normally distributed with mean 23 feet and standard deviation 4 feet. Suppose Steve encounters an adult male killer whale in the open ocean.

Question

The length of an adult male killer whale is normally distributed with mean 23 feet and standard deviation 4 feet. Suppose Steve encounters an adult male killer whale in the open ocean. (a) What is the probability that the killer whale will have a length greater than 30 feet? (b) What is the probability that the killer whale will have a length between 21 feet and 28 feet?

Answer 1

x = length

x is N(23,4) - mean 23 and SD 4

z-stat = (x-mean)/SD = (x-23)/4 is N(0,1) - mean 0 SD 1 - can use z-stat to find probability from standard normal distribution table

a)

P(x > 30) = P(z > (30-23)/4) = P(z > 1.75) = 1 - P(z < 1.75) = 1 - 0.9599 = 0.0401

b)

P(21 < x < 28) = P((21-23)/4 < z < (28-23)/4) = P(-0.5 < z < 1.25) = P(z < 1.25) - P(z < -0.5) = 0.8944 - 0.3085 = 0.5859