Question

Automobile Workers A worker in the automobile industry works an average of 42.6 hours per week. If the distribution is approximately normal with astandard deviation of 1.8 hours, what is the probability that a randomly selected automobile worker works less than 40 hours per week? Use aTI-83 Plus/TI-84 Plus calculator. Round the answer to at least four decimal places.P (X <40) =

Answer 1

Step-by-step explanation:

standard deviation = σ = 1.8 hours

average = mean = μ = 42.6 hours

Probability that a randomly selected automobile worker works less than 40 hours per week:

P(X < 40)

We apply the z score formula:

`\begin{gathered} z=(X-\mu)/(\sigma) \\ \text{let X = 40} \end{gathered}`
`\begin{gathered} z\text{ = }(40-42.6)/(1.8) \\ z\text{ = }(-2.6)/(1.8) \\ z\text{ = }-1.4444 \\ \\ P(X<\text{ 40})\text{ = P}(z\text{ < }-1.4444) \end{gathered}`
`\begin{gathered} p\text{ value of z }=\text{ -1.4444} \\ p\text{ value is 0}.074369 \end{gathered}`