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poizon [28]
3 years ago
9

The U.S. Bureau of Labor Statistics reports that of persons who usually work full-time, the average number of hours worked per w

eek is 43.4. Assume that the number of hours worked per week for those who usually work full-time is normally distributed. Suppose 12% of these workers work more than 48 hours. Based on this percentage, what is the standard deviation of number of hours worked per week for these workers?
Mathematics
1 answer:
alukav5142 [94]3 years ago
6 0

Answer:

The standard deviation of number of hours worked per week for these workers is 3.91.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by

Z = \frac{X - \mu}{\sigma}

After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X. Subtracting 1 by the pvalue, we This p-value is the probability that the value of the measure is greater than X.

In this problem we have that:

The average number of hours worked per week is 43.4, so \mu = 43.4.

Suppose 12% of these workers work more than 48 hours. Based on this percentage, what is the standard deviation of number of hours worked per week for these workers.

This means that the Z score of X = 48 has a pvalue of 0.88. This is Z between 1.17 and 1.18. So we use Z = 1.175.

Z = \frac{X - \mu}{\sigma}

1.175 = \frac{48 - 43.4}{\sigma}

1.175\sigma = 4.6

\sigma = \frac{4.6}{1.175}

\sigma = 3.91

The standard deviation of number of hours worked per week for these workers is 3.91.

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