Question

The average salary of merchandisers is $54,000 per year with a standard deviation of $6000. a. What is the probability that a merchandiser earns more than $66,000 per year? (Round z-score computation to 2 decimal places and the final answer to 4 decimal places.) Probability 0.5228 b. What is the probability that a merchandiser earns less than $42,000 per year? (Round z-score computation to 2 decimal places and the final answer to 4 decimal places.) Probability 0.5228 c. What is the probability that a merchandiser earns between $50,000 and $58,000 per year? (Round z-score computation to 2 decimal places and the final answer to 4 decimal places.) Probability 0.4972 d. What is the probability that a merchandiser will earn between $45,000 and $63,000 per year? (Round z-score computation to 2 decimal places and the final answer to 4 decimal places.) Probability 0.8664 e. What is the average salary below which 25% of the merchandisers earn? (Round the final answer to the nearest whole number.) Salary $

Answer 1

Solution:

The average salary of merchandisers is $54,000 per year with a standard deviation of $6000.

Given that, Mean Salary =M = $54000, Standard Deviation = SD = $6000

A) the probability that a merchandiser earns more than $66,000 per year is:

Here, S = 66000

Z value = (S - M)/SD = (66000-54000) / 6000 = 2

P(z ≤ 2) = 0.9772

Probability that a merchandiser earns more than $66,000 per year

= 1 - P(z ≤ 2) = 1 - 0.9772 = 0.0228 = 2.28%

B) the probability that a merchandiser earns less than $42,000 per year is:

Here, S = 42,000

Z value = (S - M)/SD = (42000-54000) / 6000 = -2

P(z ≤ -2) = 0.0236

Probability that a merchandiser earns less than $42,000 per year

= P(z ≤ -2) = 0.0236 = 2.36%

C) the probability that a merchandiser earns between $50,000 and $58,000 per year is:

S1 = $50000

Z value = (S 1- M)/SD = (50000-54000) / 6000 = -0.67

P(z ≤ -0.67) = 0.2518

S2 = $58000

Z value = (S 1- M)/SD = (58000-54000) / 6000 = 0.67

P(z ≤ 0.67) = 0.7486

Probability that a merchandiser earns between $50,000 and $58000 per year

= P(z ≤ 0.67) - P(z ≤ -0.67) = 0.7486 - 0.2518  = 0.4968 = 49.68%

D) the probability that a merchandiser will earn between $45,000 and $63,000 per year is:

S1 = $45000

Z value = (S 1- M)/SD = (45000-54000) / 6000 = -1.5

P(z ≤ -1.5) = 0.0676

S2 = $63000

Z value = (S 1- M)/SD = (63000-54000) / 6000 = 1.5

P(z ≤ 1.5) = 0.9332

Probability that a merchandiser earns between $45,000 and $63000 per year

= P(z ≤ 1.5) - P(z ≤ -1.5) = 0.9332 – 0.0676 = 0.8656 = 86.56%