Question 1

Find the range, variance, and standard deviation for the given data. The table below shows the average points scored per game by several intramural softball teams. Round to one decimal place.
$\begin{array}{c|c}
\text { Team } & \text { Points } \
\hline \text { Bombers } & 5.9 \
\text { Crunchers } & 10.9 \
\text { Homers } & 15.7 \
\text { Pelters } & 9.9 \
\text { Smackers } & 14.9 \
\text { Whoppers } & 7.5
\end{array}$

Accepted Answer

The answer of Find the range, variance, and standard deviation...

Question 2

$$\begin{array}{l}
\text { Use the equation of the regression line to predict } y \text { when } x = 20 \text {. }\
\begin{array} { c | c c c c c c } 
x & 5 & 8 & 6 & 10 & 12 & 9 \
\hline y & 18 & 20 & 15 & 25 & 30 & 25
\end{array}
\end{array}$$

Accepted Answer

The answer of \[\begin{array}{l}
\text { Use the equation of the...

Question 3

A data set of size 22 has correlation coefficient of r = -0.461. Test the significance of r at the 5% level and at the 1% level.

Accepted Answer

The critical value for r with 20 degrees of freedom (n-2) at the 5% level is approximately ±0.423, and at the 1% level is approximately ±0.537. Since -0.461 is less than -0.423 but greater than -0.537, r is significant at the 5% level but not at the 1% level.

Question 4

Find the area under the normal distribution curve between z = -0.90 and z = 3.05.

Accepted Answer

The area under the normal distribution curve between z = -0.90 and z = 3.05 is found by calculating the cumulative probability for each z-value and subtracting them. The cumulative probability for z = -0.90 is approximately 0.1841 and for z = 3.05 is approximately 0.9981. Subtracting these gives 0.9981 - 0.1841 = 0.814, which is closest to 0.815.

Question 5

Kate scored in the 35th percentile rank on an exam. If 200 students took the exam, how many students scored lower than Kate?

Accepted Answer

The 35th percentile means that Kate scored better than 35% of the students. 35% of 200 students is 70 students.

Question 6

Fran's percentile rank on an exam in a class of 500 is 85. Kelly's class rank is 60. Who is ranked higher?

Accepted Answer

The answer of Fran's percentile rank on an exam in...

Question 7

If a student's rank in a class of 500 students is 345, find the student's percentile rank.

Accepted Answer

Percentile rank is calculated as [(500 - 345) / 500] * 100 = 31%.

Question 8

$$\begin{array}{l}
\text { Find the value for } r \text { and test the significance of } r \text { at the } 5 \% \text { level and at the } 1 \% \text { level. }\
\begin{array} { c | c c c c } 
x & 21 & 14 & 18 & 23 \
\hline y & 9 & 1 & 5 & 11
\end{array}
\end{array}$$

Accepted Answer

The correlation coefficient r is calculated to be 0.998, which is very close to 1, indicating a strong positive linear relationship. Given the small sample size (n=4), the critical values for significance at both the 5% and 1% levels are lower than 0.998, making r significant at both levels.

Question 9

Find the area under the normal distribution curve to the right of z = -0.55.

Accepted Answer

The area to the right of z = -0.55 is found by looking up the z-score in a standard normal distribution table or using a calculator. The area to the left of z = -0.55 is approximately 0.291, so the area to the right is 1 - 0.291 = 0.709.

Question 10

$$\begin{array}{l}
\text { Find the value for the correlation coefficient } r \text {. }\
\begin{array} { c | c c c c c } 
x & 5 & 1 & 4 & 2 & 3 \
\hline y & 8 & 12 & 7 & 4 & 3
\end{array}
\end{array}$$

Accepted Answer

The answer of \[\begin{array}{l}
\text { Find the value for the...

Question 11

Find the mode. 5 8 2 3 10 4 28 6 17 22

Accepted Answer

The mode is the number that appears most frequently in a data set. In this list, each number appears only once, so there is no mode.

Question 12

Find the mean. 58 3 7 26 5 1 1 12 2 6

Accepted Answer

The answer of Find the mean. 58 3 7 26...

Question 13

$$\begin{array}{l}
\text { Find the equation of the regression line. }\
\begin{array} { c | c c c c c c } 
x & 12 & 14 & 10 & 9 & 15 & 8 \
\hline y & 29 & 35 & 28 & 23 & 36 & 18
\end{array}
\end{array}$$

Accepted Answer

The regression line is calculated using the formula $ y = a + bx $, where $ b $ is the slope and $ a $ is the y-intercept. Calculating these from the given data, the slope $ b $ is approximately 2.4 and the intercept $ a $ is approximately 1.2, leading to the equation $ y = 1.2 + 2.4x $.

Question 14

$$\begin{array}{l}
\text { Use a scatter plot to determine the relationship between the } x \text { values and the } y \text { values. }\
\begin{array} { c | c c c c c c c } 
x & 7 & 2 & 4 & 5 & 1 & 6 & 3 \
\hline y & 5 & 26 & 20 & 15 & 30 & 12 & 25
\end{array}
\end{array}$$

Accepted Answer

The answer of \[\begin{array}{l}
\text { Use a scatter plot to...

Question 15

For the 20 test scores shown, find the percentile rank for a score of 66. 75 63 92 74 86 50 77 82 98 65 71 89 75 66 87 59 70 83 91 73

Accepted Answer

The answer of For the 20 test scores shown, find...

Question 16

$$\begin{array}{l}
\text { Find the equation of the regression line. }\
\begin{array} { c | c c c c c c } 
x & 10 & 8 & 7 & 12 & 14 & 5 \
\hline y & 20 & 19 & 17 & 25 & 28 & 9
\end{array}
\end{array}$$

Accepted Answer

The correct equation of the regression line is found by calculating the slope and intercept using the given data points. The slope (b) is calculated as 1.9 and the intercept (a) as 1.7, leading to the equation y = 1.7 + 1.9x.

Question 17

Find $Q _ { 1 } , Q _ { 2 }$, and $Q _ { 3 }$ for the data set below.
$\begin{array} { l l l l l l l l l l } 5.4 & 2.0 & 6.8 & 3.1 & 2.9 & 4.7 & 2.1 & 5.0 & 1.9 & 3.4 \end{array}$

A) $Q _ { 1 } = 2.05 , Q _ { 2 } = 3.1 , Q _ { 3 } = 5.2$

в) $Q _ { 1 } = 2.05 , Q _ { 2 } = 3.25 , Q _ { 3 } = 5.2$

C) $Q _ { 1 } = 2.1 , Q _ { 2 } = 3.25 , Q _ { 3 } = 5.0$

D) $Q _ { 1 } = 2.1 , Q _ { 2 } = 3.4 , Q _ { 3 } = 5.0$

Accepted Answer

The answer of Find \(Q _ { 1 } ,...

Question 18

The average amount customers at a certain grocery store spend yearly is $813.71. Assume the variable is normally distributed. If the standard deviation is $71.37, find the probability that a randomly selected customer spends between $638.85 and $942.18.

Accepted Answer

The Z-scores for $638.85 and $942.18 are -2.45 and 1.80, respectively. The probability of a Z-score between -2.45 and 1.80 is approximately 0.957 or 95.7%.

Question 19

The average hourly wage of employees of a certain company is $14.26. Assume the variable is normally distributed. If the standard deviation is $4.99, find the probability that a randomly selected employee earns less than $9.27.

Accepted Answer

The answer of The average hourly wage of employees of...

Question 20

Twelve students took a placement exam with the following results. 88 65 98 71 72 94 41 86 45 49 59 75 What is the percentile rank of 71? Round to the nearest percentile.

Accepted Answer

The answer of Twelve students took a placement exam with...

Quiz 12: Voting Methods

$\begin{array}{l}\text { Use the equation of the regression line to predict } y \text { when } x = 20 \text {. }\\\begin{array} { c | c c c c c c } x & 5 & 8 & 6 & 10 & 12 & 9 \\\hline y & 18 & 20 & 15 & 25 & 30 & 25\end{array}\end{array}$