Question

Builtrite Furniture has calculated the average weekly payroll to be $15,000 with a standard deviation of $3,000. What is the probability of a weekly payroll being between $11,250 and $12,600?(Assume a normal distribution.)

15.1%

13.9%

12.8%

10.6%

Answer 1

Z-Score = (x-Mean)/Standard Deviation

Where, x = 11250 & 12600, Mean = 15000, Standard Deviation = 3000

Therefore,

For 11250, Z = (11250-15000)/3000 = -1.25

For 12600, Z = (12600-15000)/3000 = -0.8

Values from table:

Z = -1.25 = 0.5-0.3944 = 0.1056

Z = -0.8 = 0.5-0.2881 = 0.2119

Therefore,

Probability that Payroll will be BELOW 12600 is 0.2119 = 21.19% and it will be BELOW 11250 is 0.1056 = 10.56%

Probability for payroll between 11250 and 12600 = 21.19%-10.56% = 10.63% = 10.6%