sample of 150 Publix cashiers showed a mean hourly wage of $ 8.00, with a standard deviation of $ 1. Give an interval that is likely to contain about 95% of the sampled cashiers' hourly wages. A. (5, 10) B. (6, 10) C. (7, 9) D. (6, 9)

Question

Mathematics

Arely Valenzuela

9 February, 23:51

sample of 150 Publix cashiers showed a mean hourly wage of $ 8.00, with a standard deviation of $ 1. Give an interval that is likely to contain about 95% of the sampled cashiers' hourly wages. A. (5, 10) B. (6, 10) C. (7, 9) D. (6, 9)

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Benton · Answer 1

B. (6, 10)

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 8

Standard deviation = 1

Give an interval that is likely to contain about 95% of the sampled cashiers' hourly wages.

By the Empirical Rule, 95% of the sampled cashiers' hourly wages will be within 2 standard deviations of the mean, so from 2 standard deviations below the mean to two standard deviations above the mean

Two standard deviations below the mean:

8 - 2*1 = 6

Two standard deviations above the mean

8 + 2*1 = 10

So the correct answer is:

B. (6, 10)