Differentiate the function y = (x+2) (x-7)^5

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