Question

Please help with his exercise and the formula so I can solve this exercise properly so I can practice from my TV with you in a weeks

Answer 1

Answer:
`T\text{he probability that the student works for less than 4 hours per week = 0.02275}`

Step-by-step explanation:

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:

`\begin{gathered} \begin{equation*} z=(X-μ)/(σ) \end{equation*} \\ \mu\text{ = mean} \\ \sigma\text{ = standard devation} \\ X=\text{ variable = 4 hours/week} \\ z\text{ = z score } \end{gathered}`
`\begin{gathered} substitute\text{ the values:} \\ z\text{ = }\frac{4\text{ - 22}}{9} \\ \\ z\text{ = }(-18)/(9) \\ \\ z\text{ = -2} \end{gathered}`

We will look for the z = -2 from the standard normal table:

`\begin{gathered} The\text{ probability value form z table = 0.02275} \\ In\text{ percentage = 2.28\%} \end{gathered}`