Suppose annual salaries for sales associates from Geoff's Computer Shack have a mean of $32,500 and a standard deviation of $2,500. a. Calculate and interpret the z-score for a sales associate who makes $36,000.
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.
c. Use the empirical rule to determine the percentage of sales associates with salaries less than $27,500.
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? Explain.

The answer is below

Step-by-step explanation:

Given that mean (μ) = $32500, standard deviation (σ) = $2500.

a) The z score is used to determine by how many standard deviations the raw score is above or below the mean. The z score is given by:

For x < 36000:

From the normal distribution table, P(x < 36000) = P(z < 1.4) = 0.9192 = 91.92%

b) One standard deviation of mean = μ ± σ = (32500 ± 2500) = (30000, 35000)

Two standard deviation of mean = μ ± 2σ = (32500 ± 2*2500) = (27500, 37500)

Empirical rule states that 68% of data falls within one standard deviation from the mean, 95% falls within two standard deviation from the mean and 99.7% falls within one standard deviation from the mean.

Hence 95% of salaries is between $27,500 and $37,500.

c) 95% of salaries is between $27,500 and $37,500.

P(x < 27500) = (100% - 95%) / 2 = 2.5%

d) If the z score is less than -3 or greater than 3, it is considered an outlier.

For x < 42000:

Hence $42000 is an outlier

step-by-step explanation:

i think something is missing in your question because y-1=(x-12) would not pass through the point (-4,-3). because if you replace x by -4 your are supposed to find y=-3 which is not the case her. if you replace x by -4 you find =-15.

i assume the right equation is y-1=1/4*(x-12) because this one is passing through both your points (if you are interested to know how i found that out i can tell you).

in this equation if i replace x by -4 i find y=-3 and if i replace x by 12, i find y=1 so the line representing this equation is passing through those 2 points.

then the standard form of the equation is finding an expression of y in function of x

y-1=1/4*(x-12)

y=x/4-3+1

y=x/4-2

hope that .

do you confirm there was a mistake in the question?