Question

I can find percentages and values using the 68-95-99.7 rule, z-scores, and the standard normal distribution.answer the questions only if you know the answer please

Answer 1

ANSWER and EXPLANATION

1) We want to find the z score for a student who had a GPA of 3.8.

To do this, we have to apply the formula for z score:

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

where:

x = score/GPA

μ = mean

σ = standard deviation

Therefore, the z score for the student with a GPA of 3.8 is:

`\begin{gathered} z=(3.8-3)/(0.6) \\ z=(0.8)/(0.6) \\ z=\text{1}.33 \end{gathered}`

2) The z score is a measure of how far away a data point is from the mean, in other words, it is a measure of how many standard deviations a data point is above or below a mean.

We can find how many standard deviations there are in a z score of -2.4 by dividing -2.4 by the standard deviation (0.6):

`\begin{gathered} (-2.4)/(0.6) \\ -4 \end{gathered}`

Therefore, since the z score is negative, we can conclude that the student's GPA is 4 standard deviations below the mean value.