Question 8 (3 points) d Suppose annual salaries for sales associates from a part

Question

Question 8 (3 points) d Suppose annual salaries for sales associates from a particular store have a mean of $32,000 and a standard deviation of $3,000. Calculate and interpret the z-score for a sales associate who makes $38,000. a. Suppose that the distribution of annual salaries for sales associates at this store is bell-shaped. Use the b. empirical rule to calculate the percentage of sales associates with salaries between $29,000 and $35,000 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? Explain .

Explanation / Answer

mu= 32000

std dev =3000

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X=38000

mu + 2*std dev= 32000+2*3000=38000

so, Z-score=2

it means sale associate with $38000 is 2 std dev away from population mean ,$32000

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B)

empirical rule states that data which fall within the one std dev away from mean covers 68% of all observations

here,mu + 1 std dev = 32000+ 1*3000=35000

mu - 1*std dev = 32000-1*3000=29000

so,percentage of sales associates with salries between 29000 and 35000 is 68%

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C)data fall within 3 std dev of mean covers 99.7 % of observation and ouside this called an outlier

here , mu + 3*std dev=32000+3*3000=$41000

but $42000>41000

so, it can be considered as an outlier

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