Question

The lengths of a certain species of beetles are normally distributed with a mean of 1.9 centimeters and a standard deviation of 0.2 centimeters.

What is the z-score of a beetle of this species with a length of 2.38 centimeters?

Answer 1

Answer: the z score is 2.4

Step-by-step explanation:

Since the lengths of the certain species of beetles are normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x - µ)/σ

Where

x = length of the beetle species.

µ = mean length

σ = standard deviation

From the information given,

µ = 1.9 centimeters

σ = 0.2 centimeters

For a species with a length of 2.38 centimeters, the z score is

z = (2.38 - 1.9)/0.2

z = 0.48/0.2

z = 2.4