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Jessica Salas, president of Salas Products, is reviewing the warranty policy for her company's new model of automobile batteries. Life tests performed on a sample of 100 batteries indicated: (1) an average life of 75 months, (2) a standard deviation of 5 months, and (3) battery life is approximately normally distributed. Approximately 95% of the batteries will last between:______
a. 70 and 80 months
b. 60 and 90 months
c. 65 and 85 months
d. 55 and 95 months

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Tundexi

Answer:

c. 65 and 85 months

Explanation:

Life tests performed on a sample of 100 batteries indicated:

(1) an average life of 75 months,

(2) a standard deviation of 5 months, and

(3) battery life is approximately normally distributed.

We create a 95% CI around mean.

If 95% is in the middle, then 5% is in the ends, 2.5% in each end.

Z score at .025 is -1.96, z score at .975 is +1.96

To convert z to battery life:

Z*sd + mean = battery life

-1.96*5 + 75 = 65.2, rounds to 65

+1.96*5 + 75 = 84.8, rounds to 85

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