Question

Find z scores for the values. Round to nearest hundredth

Answer 1

For any normally distributed random variable (X), the z-score corresponding to any particular value of the random variable is given by the formula,

`z=(x-\mu)/(\sigma)`

The mean of the normal distribution is 425,

`\mu=425`

The standard deviation of the normal distribution is 51,

`\sigma=51`

Then the formula of z-score becomes,

`z=(x-425)/(51)`

a)

Given the value of the random variable as 268,

`x=268`

The corresponding z-score will be,

`\begin{gathered} z=(268-425)/(51) \\ z\approx-3.08 \end{gathered}`

Thus, the required z-score is -3.08 approximately.

b)

Given the value of the random variable as 512,

`x=512`

The corresponding z-score will be,

`\begin{gathered} z=(512-425)/(51) \\ z\approx1.70 \end{gathered}`

Thus, the required z-score is 1.70 approximately.

c)

Given the value of the random variable is 450,

`x=450`

The corresponding z-score will be,

`\begin{gathered} z=(450-425)/(51) \\ z\approx0.49 \end{gathered}`

Thus, the required z-score is 0.49 approximately.