Question

The lengths of mature trout in a local lake are approximately normally distributed with a mean of μ=13.7 inches, and a standard deviation of σ=1.8 inches.

1. Find the z-score corresponding to a fish that is 12.1 inches long. Round your answer to the nearest hundredth as needed.
   1. z=________

1. How long is a fish that has a z-score of 1.4? Round your answer to the nearest tenth as needed._______

Answer 1

Solution :

Given that,

mean = = 13.7

standard deviation = = 1.8

a ) x = 12.1

Using z-score formula,

z = x - /  

= 12.1- 13.7 / 1.8

= -1.6 /1.8

= -0.89

z-score = - 0.89

b ) z = 1.4

Using z-score formula,

x = z * +

= 1.4 * 1.8 + 13.7

= 16.22

x = 16.22