Question

The life span of fruit fly have a bell shaped distribution, with a mean of 32 days and a standard deviation of 5 days. What is the Z score of the fruit flys at 37 ,30 and 47 days

Answer 1

The Z-score (also known as a standard score) represents the number of standard deviations a value is away from the mean of a distribution. The formula for the Z-score is:

Z = (X - μ) / σ

Where X is the value of interest, μ is the mean of the distribution, and σ is the standard deviation of the distribution.

Given the information in the problem, we know that the mean of the fruit fly's lifespan is 32 days and the standard deviation is 5 days.

To find the Z-score of a fruit fly whose lifespan is 37 days:

Z = (37 - 32) / 5 = 1

To find the Z-score of a fruit fly whose lifespan is 30 days:

Z = (30 - 32) / 5 = -0.4

To find the Z-score of a fruit fly whose lifespan is 47 days:

Z = (47 - 32) / 5 = 2.4

Therefore, a fruit fly whose lifespan is 37 days has a Z-score of 1, a fruit fly whose lifespan is 30 days has a Z-score of -0.4, and a fruit fly whose lifespan is 47 days has a Z-score of 2.4.