Answers26.27 TCEC ALGEBRA 2.1Applications with Standard Normal DistributionQuestion 10
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Applications with Standard Normal Distribution

Question 10 • 26.27 TCEC ALGEBRA 2.1

The life of a certain brand of battery is normally distributed, with mean 128 hours and standard deviation 16 hours. What is the probability that a battery you buy lasts at most 100 hours? Standardize the variable.x = 100 is equivalent to z = –0.570.57–1.751.75.

Answer
A
–0.57
B
0.57
C
–1.75
D
1.75

Explanation

Standardize using z = (x − μ)/σ. For x = 100, mean μ = 128, and standard deviation σ = 16, z = (100 − 128)/16 = −28/16 = −1.75. So 100 hours corresponds to z = −1.75, choice C.

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