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# The results of a question asked in a simple random survey are reported in the accompanying table.

I need help with part "D" below, please.

The results of a question asked in a simple random survey are reported in the accompanying table. The question asked was​ "If you own a cell​ phone, what was your cell phone bill last​ month? Express answers to the​ penny." Use the data to complete parts​ (a) through​ (d) below.

Click the icon to view the table of cell phone bills.

​(a) Draw a histogram of the data and comment on the shape.

Choose the correct histogram below.

A.

230

0

460

0

4

8

12

16

20

24

Cell phone bill (\$)

Frequency

A histogram has a horizontal axis labeled "Cell phone bill (dollars)" from 0 to 460 in increments of 20 and vertical axis labeled "Frequency" from 0 to 24 in increments of 2. Vertical bars with class width 20 are plotted with heights as follows, with class listed first and height listed second: 0 to 20, 7; 20 to 40, 8; 40 to 60, 16; 60 to 80, 18; 80 to 100, 12; 100 to 120, 14; 120 to 140, 3; 140 to 160, 9; 160 to 180, 4; 180 to 200, 3; 200 to 220, 3; 240 to 260, 1; 360 to 380, 1; 420 to 440, 1.

B.

230

0

460

0

4

8

12

16

20

24

Cell phone bill (\$)

Frequency

A histogram has a horizontal axis labeled "Cell phone bill (dollars)" from 0 to 460 in increments of 20 and vertical axis labeled "Frequency" from 0 to 24 in increments of 2. Vertical bars with class width 20 are plotted with heights as follows, with class listed first and height listed second: 20 to 40, 2; 140 to 160, 1; 180 to 200, 3; 200 to 220, 3; 220 to 240, 4; 240 to 260, 9; 260 to 280, 3; 280 to 300, 14; 300 to 320, 11; 320 to 340, 17; 340 to 360, 18; 360 to 380, 8; 380 to 400, 4; 400 to 420, 3.

C.

230

0

460

0

4

8

12

16

20

24

Cell phone bill (\$)

Frequency

A histogram has a horizontal axis labeled "Cell phone bill (dollars)" from 0 to 460 in increments of 20 and vertical axis labeled "Frequency" from 0 to 24 in increments of 2. Vertical bars with class width 20 are plotted with heights as follows, with class listed first and height listed second: 0 to 20, 6; 20 to 40, 4; 40 to 60, 10; 60 to 80, 3; 80 to 100, 14; 100 to 120, 11; 120 to 140, 17; 140 to 160, 18; 160 to 180, 9; 180 to 200, 4; 200 to 220, 3; 220 to 240, 1.

Comment on the shape of the histogram. Choose the correct answer below.

A.

The histogram is symmetric and​ bell-shaped.

B.

The histogram is uniform.

​(b) Draw a boxplot of the data. Are there any​ outliers?

Choose the correct boxplot below.

A.

0

120

240

360

Cell Phone Bill (\$)

A boxplot is plotted over a horizontal number line labeled from less than 0 to 360 plus in increments of 40. The boxplot consists of the following: a box with left and right edges at 55 and 120; a vertical line inside the box at 80; horizontal lines extending out from the box's left and right edges to 0 and 250, respectively; and two asterisks plotted at 370 and 435. All values are approximate.

B.

0

120

240

360

Cell Phone Bill (\$)

A boxplot is plotted over a horizontal number line labeled from less than 0 to 360 plus in increments of 40. The boxplot consists of the following: a box with left and right edges at 0 and 60, a vertical line inside the box at 50, and a horizontal line extending out from the box's right edge to 435. All values are approximate.

C.

0

120

240

360

Cell Phone Bill (\$)

A boxplot is plotted over a horizontal number line labeled from less than 0 to 360 plus in increments of 40. The boxplot consists of the following: a box with left and right edges at 55 and 120; a vertical line inside the box at 80; horizontal lines extending out from the box's left and right edges to 0 and 200, respectively; and three asterisks plotted at 250, 370, and 435. All values are approximate.

Are there​ outliers?

​No, because there are no values that fall outside​ 1.5(IQR) of Upper Q 1

Q1 and Upper Q 3

Q3.

​No, because there are no values that are more extreme than Upper Q 1

Q1 or Upper Q 99

Q99.

​Yes, because there are several values that are more extreme than Upper Q 1

Q1 or Upper Q 99

Q99.

​Yes, because there are several values that fall outside​ 1.5(IQR) of Upper Q 1

Q1 and Upper Q 3

Q3.

​(c) Based on the results to parts​ (a) and​ (b), explain why a large sample size might be desirable to construct a confidence interval for the mean monthly cell phone bill. Choose the correct answer below.

A.

The results to parts​ (a) and​ (b) indicate that the underlying population is normal. Such populations require large sample sizes to construct valid confidence intervals.

B.

The results to parts​ (a) and​ (b) indicate that the sample data are not independent. Dependent samples require large sample sizes to construct valid confidence intervals.

C.

The results to parts​ (a) and​ (b) indicate that the sample size is small relative to the population size. Sample sizes must be large relative to the population size to construct valid confidence intervals.

D.

The results to parts​ (a) and​ (b) indicate that the underlying population is​ non-normal. Such populations require large sample sizes to construct valid confidence intervals.

​(d) Use statistical software to construct a 99

99​% confidence interval for the mean monthly cell phone bill.

​(\$

77.67

77.67​, ​\$

113.43

113.43​)

​(Round to two decimal places as​ needed.)

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