What percentage of people in this profession earn annual salaries between $54,000 and $57,000? Round your result to one decimal place

Question

The annual salaries for people in a particular profession are known to be normally distributed with a mean of $54,800 and a standard deviation of $2,600.

What percentage of people in this profession earn annual salaries between $54,000 and $57,000? Round your result to one decimal place

Answer 1

Determine z-scores to standardize the normal distribution

(57000-54800)/2600 ≈ 0.84

(54000-54800)/2600 ≈ -0.31

Determine the percentage between the z-scores

P(-0.31<Z<0.84) = P(Z<0.84)-P(Z<-0.31) ≈ 0.7995-0.3783 = 0.4212 ≈ 42.1%

Therefore, 42.1% of people in this profession earn annual salaries between $54,000 and $57,000.

Hope this helped! Make sure to use a z-table to determine the percentage value.