Question

the annual salaries at a particular company are approximately normally distributed with a mean of $100,000 and a standard deviation of ,000. find the proportion of employees that earn between q,000 and 9,000

Answer 1

The annual salaries at a particular company are approximately normally distributed with a mean is 0.42124

Manufacturing job :

Mean (m) = 40,000

Standard deviation (s) = 9000

Sales job :

Mean (m) = 35000

Standard deviation (s) = 9000

Probability of earning more than 45000 if one or the other job is selected;

Obtaining the standardized scores and probability for each :

Z = (x - m) / s

P(x > 45000)

Z = (45000 - 40000) / 9000 = 0.5555

= 0.56

P(Z > 0.56) = 0.28774(Z probability calculator)

For sales

P(x > 45000)

Z = (45000 - 35000) / 9000 = 1.1111111

= 1.11

P(Z > 1.11) = 0.1335 (Z probability calculator)

0.28774 + 0.1335 = 0.42124

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