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:

it's equivalent, so we can say that its equal.

let's call the denominator x and the numerador is 18 less then denominator, x - 18.

multiply

2.x = 5.(x - 18)

2x = 5x - 90

90 = 5x - 2x

90 = 3x

x = 90/3

x = 30

so:

"it's not the heat, it's the humidity".   that's a partly valid phrase you may have heard in the summer, but it's actually both.   the heat index, also known as the apparent temperature, is what the temperature feels like to the human body when relative humidity is combined with the air temperature.   this has important considerations for the human body's comfort.   when the body gets too hot, it begins to perspire or sweat to cool itself off.   if the perspiration is not able to evaporate, the body cannot regulate its temperature.   evaporation is a cooling process.   when perspiration is evaporated off the body, it effectively reduces the body's temperature.   when the atmospheric moisture content (i.e. relative humidity) is high, the rate of perspiration from the body decreases.   in other words, the human body feels warmer in humid conditions.   the opposite is true when the relative humidity decreases because the rate of perspiration increases.   the body actually feels cooler in arid conditions.   there is direct relationship between the air temperature and relative humidity and the heat index, meaning as the air temperature and relative humidity increase (decrease), the heat index increases (decreases).

step-by-step explanation: