4. The average American last year worked 44 hours per week and a population standard deviation of 7 hours. What percentage of people work at least 50 hours per week? What percentage of people work less than 35 hours per week? How many hours does someone need to work to be in the upper 5% of hours worked per week?

a) 19.6%

b) 9.93%

c) 55.515 hours

Step-by-step explanation:

The average American last year worked 44 hours per week and a population standard deviation of 7 hours.

We solve using z score formula

z = (x-μ)/σ, where x is the raw score, μ is the population mean, and σ is the population standard deviation.

a) What percentage of people work at least 50 hours per week?

At least means greater than or equal to

z = 50 - 44/7

z = 0.85714

P-value from Z-Table:

P(x<50) = 0.80432

P(x>50) = 1 - P(x<50) = 0.19568

Converting to Percentage

= 0.19568 × 100

= 19.568

= 19.6%

b) What percentage of people work less than 35 hours per week?

z = 35 - 44/7

z = -1.28571

P-value from Z-Table:

P(x<35) = 0.099271

Converting to percentage

= 0.099271 × 100

= 9.9271 %

= 9.93%

c) How many hours does someone need to work to be in the upper 5% of hours worked per week?

Upper 5% = 95%

z-score for 95th percentile = 1.645

Hence:

1.645 = x - 44/7

Cross Multiply

1.645 × 7 = x - 44

x = 44 + (1.645 × 7)

x = 44 + 11.515

x = 55.515 hours