Answer:
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
