Question

Calculate the data value that corresponds to each of the following z-scores.

a. Final exam scores: Allison’s z-score = 2.30, μ = 74, σ = 7.
b. Weekly grocery bill: James’ z-score = –1.45, μ = $53, σ = $12.
c. Daily video game play time: Eric’s z-score = –0.79, μ = 4.00 hours, σ = 1.15 hours.

Answer 1

Answer:

a) 90.1

b) $35.6

c) 3.0915 hours

Step-by-step explanation:

The z-score measures how many standard deviations a score X is above or below the mean.

It is given by the following formula:

$Z = \frac{X - \mu}{\sigma}$

In which $\mu$ is the mean and $\sigma$ is the standard deviaition.

In all three cases, we have to find X

a. Final exam scores: Allison’s z-score = 2.30, μ = 74, σ = 7.

$Z = \frac{X - \mu}{\sigma}$

$2.30 = \frac{X - 74}{7}$

$X - 74 = 7*2.3$

$X = 90.1$

b. Weekly grocery bill: James’ z-score = –1.45, μ = $53, σ = $12.

$Z = \frac{X - \mu}{\sigma}$

$-1.45 = \frac{X - 53}{12}$

$X - 53 = -1.45*12$

$X = 35.6$

Mean and standard deviation in dollars, so the answer also in dollars.

c. Daily video game play time: Eric’s z-score = –0.79, μ = 4.00 hours, σ = 1.15 hours.

$Z = \frac{X - \mu}{\sigma}$

$-0.79 = \frac{X - 4}{1.15}$

$X - 4 = -0.79*1.15$

$X = 3.0915$

Mean and standard deviation in hours, answer in hours.