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# Normal Probability

4. A tool industry publication claims that the average salary for executives is \$129,500 and the standard deviation of all salaries in the industry is \$13,500, a study of 20 executives finds that the average salary is \$136, 700 with a standard deviation of \$22,570.

(5) Identify: = _________, s = __________, ? = _________, Ï? = _________, n = __________

5. In one region, the September energy consumption data for single-family homes are found to be normally distributed with a mean of 1050 kilowatts (kW) and a standard deviation of 218 kW

a) (2) What is the probability that a single-family home in that region used more than 1075 kW?

b) (2) If 50 different homes were randomly selected, what is the value of the standard error (i.e. standard deviation of the sampling distribution)

c) (4) For the sample of 50 different, randomly selected homes, find the probability that their mean energy consumption level for September was greater than 1075 kW?

d) (4) Compare the results for part A and part C, and explain why the probabilities changed.

#### Solution Preview

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4. A tool industry publication claims that the average salary for executives is \$129,500 and the standard deviation of all salaries in the industry is \$13,500, a study of 20 executives finds that the average salary is \$136, 700 with a standard deviation of \$22,570.

(5) Identify: = __\$136, 700__, s = __\$22,570__, μ = _ \$129,500__,

σ = _\$13,500_, n = __20__

5. In one region, the September energy consumption data for ...

#### Solution Summary

The solution provides step-by-step method for the calculation of probability using the Z score. Formula for the calculation and Interpretations of the results are also included.

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