Question

1.Find the population mean or sample mean as indicated. Population: 7, 8​,18​,19​,13. The population mean is? (type an integer or decimal rounded to three decimal places as needed) .Find the sample standard deviation.

4​, 58​, 11​, 49​, 37​, 23​, 30​, 27​, 30​, 29

S= ? ( round to one decimal place as needed)

4.An insurance company crashed four cars in succession at 5 miles per hour. The cost of repair for each of the four crashes was ​$430​, ​$457​, ​$418​, ​$233. Compute the​ range, sample​ variance, and sample standard deviation cost of repair.
The range is ​$?
s2=?
​(Round to the nearest whole number as​ needed.)
s=​$?
​(Round to two decimal places as​ needed.)

7. Esther and George want to make trail mix.trail mix. In order to get the right balance of ingredients for their tastes they bought 4 pounds of raisins at $ 3.41 per pound, 2 pounds of peanuts for $4.95 per pound, 2 pounds of chocolate chips for $ 3.59$3.59 per pound. Determine the cost per pound of the trail mix. The cost per pound of the trail mix is?( Round to the nearest cent)

13.For the data set​ below,
​(a) Determine the​ least-squares regression line.
​(b) Graph the​ least-squares regression line on the scatter diagram.

x 5 6 7 8 10   
y 8 10 10 14 19
  
​(a) Determine the​ least-squares regression line.
y= ? x+? ​(Round to four decimal places as​ needed.)

14.An engineer wants to determine how the weight of a​ car, x, affects gas​ mileage, y. The following data represent the weights of various cars and their miles per gallon.
Car: A, B,C,D,E

Weight​ (pounds), x 2530, 3105, 3440, 3755, 4050

Miles per​ Gallon, y 27.9, 23.3, 24.5, 18.3, 19.4

​(a) Find the​ least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable.
Write the equation for the​ least-squares regression line.
y=?x+?
​(Round the x coefficient to five decimal places as needed)
​(b) Interpret the slope and​ intercept, if appropriate.
Choose the best interpretation for the slope.
A.The slope indicates the ratio between the mean weight and the mean miles per gallon.
B.The slope indicates the mean miles per gallon.
C.The slope indicates the mean weight.
D.The slope indicates the mean change in miles per gallon for an increase of 1 pound in weight.
E.It is not appropriate to interpret the slope because it is not equal to zero.

Choose the best interpretation for the​ y-intercept.
A.The​ y-intercept indicates the miles per gallon of the lightest car in the population.
B.The​ y-intercept indicates the miles per gallon for a new car.
C.The​ y-intercept indicates the mean miles per gallon for a car that weighs 0 pounds.
D.The​ y-intercept indicates the mean miles for a car that weighs 0 pounds.
E.It is not appropriate to interpret the​ y-intercept because it does not make sense to talk about a car that weighs 0 pounds.
​
(c) Predict the miles per gallon of car D and compute the residual. Is the miles per gallon of this car above average or below average for cars of this​ weight?

A.It is aboveabove average.

B.It is belowbelow average.

The predicted value is ? miles per gallon( Round to two decimal places as needed)

The residual is ? miles per gallon(Round to two decimal places as needed)

Answer 1

Solution : ( 1 )

7, 8​,18​,19​,13

and

4​, 58​, 11​, 49​, 37​, 23​, 30​, 27​, 30​, 29

Sample Mean :

and

Sample standard deviation :

data	data-mean	(data - mean)2
4	-25.8	665.64
58	28.2	795.24
11	-18.8	353.44
49	19.2	368.64
37	7.2	51.84
23	-6.8	46.24
30	0.2	0.04
27	-2.8	7.84
30	0.2	0.04
29	-0.8	0.64

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Solution : ( 4 )

$430​, ​ $457​, ​$418​, ​ $233

data	data-mean	(data - mean)2
430	45.5	2070.25
457	72.5	5256.25
418	33.5	1122.25
233	-151.5	22952.25

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Solution : ( 7 )

4 pounds * $3.41/pound = $13.64 for the raisins.
2 pounds * $4.95/pound = $9.9 for the peanuts.
2 pounds * $3.59/pound = $7.18 for the chocolate chips.

$13.64 + $9.9 + $7.18 = $ 30.72 cost for all trail mix.
4 + 2 + 2 = 8 pounds of trail mix.

The cost per pound is = $30.72/8 = $ 3.84

Hence, the cost per pound of the trail mix is $ 3.84

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Solution : ( 13 )

X	Y	X * Y	X * X
5	8	40	25
6	10	60	36
7	10	70	49
8	14	112	64
10	19	190	100

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Solution : ( 14 )

X	Y	X * Y	X * X
2530	27.9	70587	6400900
3105	23.3	72346.5	9641025
3440	24.5	84280	11833600
3755	18.3	68716.5	14100025
4050	19.4	78570	16402500

and