Question

Assume that you have a choice between a manufacturing job and a sales job. The annual earnings from the manufacturing job will have a normal distribution with a mean of $40 000 and a standard deviation of $9 000. The annual earnings from the sales job will have a normal distribution with a mean of $35 000 and a standard deviation of $9 000. What is the probability that you would earn more than $45 000 per year if you select one or the other

Answer 1

Answer:

0.42124

Step-by-step explanation:

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