Question

Suppose the teenagers that attend public high schools get an average of 5.7hours of sleep each night with a standard deviation of 1.7 hours. Assume that the average sleep hour is normally distributed, and 35 high school students are randomly selected. Compute the z-score for 6 hours of sleep.

A. 1.04
B. 0.18
C. 0.52
D. 0.82

Answer 1

The z score for 6 hours of sleep based on the information provided above is 0. 18 (Option B). See the calculations below.

How do you calculate Z-Score?

Step 1 ................The formula for Z-Score is given as:

Z = (x-μ)/σ

Where

Z = Standard Score

x = Observed Value

μ = mean of the sample; and

σ = Standard Deviation of the sample.

Note that

• the observed value is (x) is 5.7;
• the standard deviation (σ ) is 1.7;
• the mean (average) (μ) is 6;

Step 2 ...................Impute the values then compute:

Hence the Z score =

(5.7-6)/1.7 = 0.17647058823

Which is approximately 0.18.

Hence the Z-Score for 35 students is 0.18 (Option B)

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