A. Student GPAs: Bob’s z-score z = + 1.71 μ = 2.98 σ = 0.36 b. Weekly work hours: Sarah’s z-score z = + 1.18 μ = 21.6 σ = 7.1 c. Bowling scores: Dave’s z-score z = - 1.35 μ = 150 σ = 40 Find the original data value corresponding to each standardized z-score. (Round your answers to 2 decimal places.)

a. Bob’s GPA
b. Sarah’s weekly work hours
c. Dave’s bowling score

a)

And replacing we got:

b)

And replacing we got:

c)

And replacing we got:

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Part a

Let X the random variable of interest for this case. We define the z score with the following formula:

And for this case we know that

If we solve for x from the z score formula we got:

And replacing we got:

Part b

Let X the random variable of interest for this case. We define the z score with the following formula:

And for this case we know that

If we solve for x from the z score formula we got:

And replacing we got:

Part c

Let X the random variable of interest for this case. We define the z score with the following formula:

And for this case we know that

If we solve for x from the z score formula we got:

And replacing we got:

the graph in the attached figure

step-by-step explanation:

we have

using a graphing tool

the graph in the attached figure

the roots are ( x-intercepts) x=-0.5,x=1,x=3

the y-intercept is the point (0,3)

where's the diagram?

step-by-step explanation: