the accompanying data represent the miles per gallon of a random sample of cars with a three - cylinder, 1.0…

the accompanying data represent the miles per gallon of a random sample of cars with a three - cylinder, 1.0 liter engine. (a) compute the z - score corresponding to the individual who obtained 38.1 miles per gallon. interpret this result. (b) determine the quartiles. (c) compute and interpret the interquartile range, iqr. (d) determine the lower and upper fences. are there any outliers? click the icon to view the data. (a) compute the z - score corresponding to the individual who obtained 38.1 miles per gallon. interpret this result. the z - score corresponding to the individual is □ and indicates that the data value is □ standard deviation(s) □ the □ (type integers or decimals rounded to two decimal places as needed.) mpg data 32.7 36.2 38.0 38.6 40.1 42.2 34.2 36.4 38.1 38.9 40.6 42.8 34.5 37.3 38.2 39.4 41.5 43.5 35.6 37.6 38.4 39.6 41.8 49.2

the accompanying data represent the miles per gallon of a random sample of cars with a three - cylinder, 1.0 liter engine. (a) compute the z - score corresponding to the individual who obtained 38.1 miles per gallon. interpret this result. (b) determine the quartiles. (c) compute and interpret the interquartile range, iqr. (d) determine the lower and upper fences. are there any outliers? click the icon to view the data. (a) compute the z - score corresponding to the individual who obtained 38.1 miles per gallon. interpret this result. the z - score corresponding to the individual is □ and indicates that the data value is □ standard deviation(s) □ the □ (type integers or decimals rounded to two decimal places as needed.) mpg data 32.7 36.2 38.0 38.6 40.1 42.2 34.2 36.4 38.1 38.9 40.6 42.8 34.5 37.3 38.2 39.4 41.5 43.5 35.6 37.6 38.4 39.6 41.8 49.2

Answer

Explanation:

Step1: Calculate the mean

The formula for the mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. Here $n = 24$, and $\sum_{i=1}^{24}x_{i}=32.7+36.2 +\cdots+49.2=919.2$. So $\bar{x}=\frac{919.2}{24}=38.3$.

Step2: Calculate the standard - deviation

The formula for the sample standard - deviation $s=\sqrt{\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n - 1}}$. First, calculate $(x_{i}-\bar{x})^{2}$ for each $x_{i}$: $(32.7 - 38.3)^{2}=(-5.6)^{2}=31.36$, $(36.2-38.3)^{2}=(-2.1)^{2}=4.41,\cdots$. $\sum_{i = 1}^{24}(x_{i}-\bar{x})^{2}=31.36 + 4.41+\cdots=249.92$. Then $s=\sqrt{\frac{249.92}{23}}\approx3.30$.

Step3: Calculate the z - score

The formula for the z - score is $z=\frac{x-\bar{x}}{s}$. Given $x = 38.1$, $\bar{x}=38.3$, and $s\approx3.30$. Then $z=\frac{38.1 - 38.3}{3.30}\approx - 0.06$. The z - score of $-0.06$ indicates that the data value is $0.06$ standard deviation(s) below the mean.

Answer:

The z - score corresponding to the individual is $-0.06$ and indicates that the data value is $0.06$ standard deviation(s) below the mean.