Given:
mean = 22 hours/week
standard deviation = 9 hours
The length of time college student's work is normally distributed
To find:
The probability that the student works for less than 4 hours per week
To determine the probability, we will convert the normal distribution to standard normal using the formula:
[tex]\begin{gathered} \begin{equation*} z=\frac{X-μ}{σ} \end{equation*} \\ \mu\text{ = mean} \\ \sigma\text{ = standard devation} \\ X=\text{ variable = 4 hours/week} \\ z\text{ = z score } \end{gathered}[/tex][tex]\begin{gathered} substitute\text{ the values:} \\ z\text{ = }\frac{4\text{ - 22}}{9} \\ \\ z\text{ = }\frac{-18}{9} \\ \\ z\text{ = -2} \end{gathered}[/tex]We will look for the z = -2 from the standard normal table:
[tex]\begin{gathered} The\text{ probability value form z table = 0.02275} \\ In\text{ percentage = 2.28\%} \end{gathered}[/tex]