Answer to Question #120088 in Statistics and Probability for Grace

Question

In a certain city the mean price of a litre of milk is 63 cents and the standard deviation is 8
cents. The average price of a loaf of bread is $1.80 and the standard deviation is 15 cents.
At a 24-hour convenience store, a litre of milk costs $0.89 and a loaf of bread costs $2.19.
a. Determine the z-score for each item. *Round your z-score to the nearest hundredth.
MILK BREAD

b. Which item costs relatively more at the convenience store? Explain your answer.

Scores on intelligence tests (IQs) are normally distributed in children. IQs from the Wechsler
intelligence tests are known to have means of 100 and standard deviations of 15.

a. A student scored 122 on the test. Determine the z-score. *Round your z-score to the nearest hundredth.

b. A different student had a z-score of 2.41. Determine this student’s actual mark, to the nearest hundredth, on the test.

Answer 1

a. Determine the z-score for each item. *Round your z-score to the nearest hundredth.

MILK

$$Z={0.89-0.63\over 0.08}=3.25$$

BREAD 

$$Z={2.19-1.80\over 0.15}=2.6$$

$\begin{matrix} MILK & BREAD \\ 3.25 & 2.6 \end{matrix}$

b.

$Z_{milk}=3.25>2.6=Z_{bread}.$

Our Z-scores show us that we are overpaying quite a bit more for the milk than we are for the bacon.

Then Milk costs relatively more at the convenience store.

a.

$$Z={122-100\over15}=1.47$$

b.

$$Z={X-100\over15}=2.41=>X=2.41(15)+100=136.15$$

A student scored $136.15$ on the test.