Question

A normally distributed variable is known to have a mean of 34 and a standard deviation of 2. Between what two values does 95% of the data lie?

O 28 and 40
O 32 and 36
O 30 and 38
O 25 and 35

Answer 1

C) 30 and 38

Explanation:

In a normal distribution, 95% of the data points fall within two standard deviations of the mean.

Given:

• mean μ = 34
• standard deviation σ = 2

To find the two values between which 95% of the data lies, subtract and add two standard deviations to the mean:

⇒ μ - 2σ = 34 - 2(2) = 34 - 4 = 30

⇒ μ + 2σ = 34 + 2(2) = 34 + 4 = 38

Therefore, 95% of the data lies between the values:

• 30 and 38.