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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) =

Automobile Workers A worker in the automobile industry works an average of 426 hours per week If the distribution is approximately normal with astandard deviati class=

Respuesta :

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:

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