Suppose annual salaries for sales associates from a particular store have a mean

Question

Suppose annual salaries for sales associates from a particular store have a mean of $32,500 and a standard deviation of $2,500.

a. Calculate the number of standard deviations a sales associates salary of $36,000 is from the mean salary.

_______ (round to one decimal place)

b. Suppose that the distribution of annual salaries for sales associates at this store is bell-shaped.  Use the empirical rule to calculate the percentage of sales associates with salaries between $27,500 and $37,500.

________ (round to the nearest whole number)

c. Use the empirical rule to determine the percentage of sales associates with salaries less than $27,500.

_________ (round to the nearest whole number)

d. Still suppose that the distribution of annual salaries for sales associates at this store is bell-shaped.  A sales associate makes $42,000.  Should this salary be considered an outlier?

__________ (yes or no)

Explanation / Answer

a) (36,000-32,500)/2,500= 1.4

b) 95% (2 standard deviations either side)

c) 2.5% (more than 2 standard deviations below the mean)

d) yes, (more than 3 standard deviations above the mean)

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