Question

The weight of laboratory mice follows a normal distribution, with a mean of 0.68 ounce and a standard deviation of 0.02 ounce. What percentage of the mice weigh between 0.62 ounce and 0.74 ounce?

A.99.7%
B.95%
C.68%
D.47.5%
E.34%

Answer 1

A.99.7%

Explanation:

We are given;

• Mean of a distribution, μ as 0.68 ounce
• Standard deviation, σ as 0.02 ounce
• The range values of X between 0.62 ounce and 0.74 ounce

We are required to calculate the percentage of the weight to be between 0.62 ounce and 0.74 ounce

Step 1: Calculate the Z-score

To get the Z-score we use the formula;

Z-score = (x-μ)/σ

Therefore, when x = 0.62

Then z score = (0.62 - 0.68 ) ÷ 0.02

= -3

When, x = 0.74

Then, Z score = (0.74 - 0.68) ÷ 0.02

= 3

Step 2: we use the Z-score table or the empirical rule

Using the Z-score table;

P(-3 < z < 3) = 99.7%.

Therefore; the percentage of mice that weigh between 0.62 ounce and 0.74 ounce is 99.7%.