Question

1. vaida is going to purchase her first new car. several items are a factor in her purchase, including fuel efficiency. she randomly selects thirty - two chevrolet vehicles from a government website that posts fuel efficiency, in miles per gallon (mpg). the summarized results are shown in the table.

n	mean	sd	min	q₁	med	q₃	max
32	25.156	3.38	21	22	25	27.5	34

which of the following is the closest to the z - score of the maximum fuel efficiency?
a) 1.61
b) 2.62
c) 2.66
d) 8.84
e) 26.557

1. the shoe size of american males is normally distributed with a mean size 10 and standard deviation of size 1.5. the shoe size of american females is normally distributed with a mean size 8.5 and standard deviation of size 1.5. jack is an american male with shoe size 9. he has the same standardized shoe size (z - score) as emmaline, an american female. what is emmaline’s shoe size?

a) 7.5
b) 8.5
c) 9
d) 9.5
e) 10

Explanation:

Question 7

Step1: Recall z - score formula

The formula for the z - score is $z=\frac{x - \mu}{\sigma}$, where $x$ is the value, $\mu$ is the mean, and $\sigma$ is the standard deviation.

Step2: Identify values

From the table, for the maximum fuel efficiency, $x = 34$, $\mu=25.156$, and $\sigma = 3.38$.

Step3: Calculate z - score

Substitute the values into the formula: $z=\frac{34 - 25.156}{3.38}=\frac{8.844}{3.38}\approx2.62$

Step1: Calculate Jack's z - score

The z - score formula is $z=\frac{x - \mu}{\sigma}$. For Jack (male), $x = 9$, $\mu = 10$, and $\sigma=1.5$. So $z=\frac{9 - 10}{1.5}=\frac{- 1}{1.5}=-\frac{2}{3}\approx - 0.6667$

Step2: Use z - score to find Emmaline's shoe size

For Emmaline (female), $\mu = 8.5$, $\sigma = 1.5$, and $z=-\frac{2}{3}$. We use the z - score formula $z=\frac{x - \mu}{\sigma}$ and solve for $x$.
Rearranging the formula: $x=\mu+z\sigma$.
Substitute the values: $x = 8.5+(-\frac{2}{3})\times1.5=8.5 - 1=7.5$

Answer:

B) 2.62

Question 8