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Using the 68-95-99.7 rule:

Assume that a set of test scores is normally distributed with a mean of 100 and a standard deviation of 20. Use the 68-95-99.7 rule to find the following quantities:
Suggest you make a drawing and label first…
a. Percentage of scores less than 100
b. Relative frequency of scores less than 120
c. Percentage of scores less than 140
d. Percentage of scores less than 80
e. Relative frequency of scores less than 60
f. Percentage of scores greater than 120

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2 answers
  1. Do you know the 68-95-99.7 rule? Approximately 68% of scores in normal distribution are within one standard deviation (34% on each side of the mean), 95% within 2 SD, and 99.7% within 3 SD.

    a. Mean = median in normal distribution, so that should tell you % less < mean.

    b. Z = number of SD above or below mean = (score-mean)/SD

    This should start you out.

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  2. The mean weekly earnings of all male workers in a state is $775 and the mean weekly earnings of all female workers in the same state is $658. Suppose we select one sample of 400 male workers and another sample of 300 female workers from this state. What is the mean of the sampling distribution of the difference between the mean weekly earnings of these two samples?

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