According to an NRF survey conducted by BIGresearch, the average family spends about $237 on electronics (computers, cell phones, etc.) in back-to-college spending per student. Suppose back-to-college family spending on electronics is normally distributed with a standard deviation of $54. If a family of a returning college student is randomly selected, what is the probability that: (a) They spend less than $150 on back-to-college electronics? (b) They spend more than $390 on back-to-college electronics? (c) They spend between $120 and $175 on back-to-college electronics?

Answers

Answer 1

Answer:

(a) Probability that a family of a returning college student spend less than $150 on back-to-college electronics is 0.0537.

(b) Probability that a family of a returning college student spend more than $390 on back-to-college electronics is 0.0023.

(c) Probability that a family of a returning college student spend between $120 and $175 on back-to-college electronics is 0.1101.

Step-by-step explanation:

We are given that according to an NRF survey conducted by BIG research, the average family spends about $237 on electronics in back-to-college spending per student.

Suppose back-to-college family spending on electronics is normally distributed with a standard deviation of $54.

Let X = back-to-college family spending on electronics

SO, X ~ Normal([tex]\mu=237,\sigma^{2} =54^{2}[/tex])

The z score probability distribution for normal distribution is given by;

                                 Z  =  [tex]\frac{X-\mu}{\sigma}[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = population mean family spending = $237

           [tex]\sigma[/tex] = standard deviation = $54

(a) Probability that a family of a returning college student spend less than $150 on back-to-college electronics is = P(X < $150)

        P(X < $150) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{150-237}{54}[/tex] ) = P(Z < -1.61) = 1 - P(Z [tex]\leq[/tex] 1.61)

                                                             = 1 - 0.9463 = 0.0537

The above probability is calculated by looking at the value of x = 1.61 in the z table which has an area of 0.9463.

(b) Probability that a family of a returning college student spend more than $390 on back-to-college electronics is = P(X > $390)

        P(X > $390) = P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{390-237}{54}[/tex] ) = P(Z > 2.83) = 1 - P(Z [tex]\leq[/tex] 2.83)

                                                             = 1 - 0.9977 = 0.0023

The above probability is calculated by looking at the value of x = 2.83 in the z table which has an area of 0.9977.

(c) Probability that a family of a returning college student spend between $120 and $175 on back-to-college electronics is given by = P($120 < X < $175)

     P($120 < X < $175) = P(X < $175) - P(X [tex]\leq[/tex] $120)

     P(X < $175) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{175-237}{54}[/tex] ) = P(Z < -1.15) = 1 - P(Z [tex]\leq[/tex] 1.15)

                                                         = 1 - 0.8749 = 0.1251

     P(X < $120) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{120-237}{54}[/tex] ) = P(Z < -2.17) = 1 - P(Z [tex]\leq[/tex] 2.17)

                                                         = 1 - 0.9850 = 0.015

The above probability is calculated by looking at the value of x = 1.15 and x = 2.17 in the z table which has an area of 0.8749 and 0.9850 respectively.

Therefore, P($120 < X < $175) = 0.1251 - 0.015 = 0.1101


Related Questions

In order to evaluate the performance of the artificial pancreas, a researcher randomly draw 5 rats as a control group, and draw other 5 rats as a treatment group. The control group did not receive the artificial pancreas, the treatment group did. The research wanted to compare the blood-sugar readings for the treatment group with those of the control group. The treatment group has a sample mean blood-sugar reading Y = 400 unit and a standard deviation Si = 80 unit. The control group has a sample mean blood-sugar reading Y, = 200 unit and a standard deviation S2 = 50 unit. Assume the population variances are not equal, calculate the standard error for the difference of the sample means Ý -Y (Round to three decimal places)

Answers

Answer: 42.190

Step-by-step explanation:

From the question, the population variances are not equal. The calculation has been attached in the picture below.

The answer is 42.190 to 3 decimal places.

اذا كانت س زاويه حاده و كان جاس= ٣/٥ فان ظا س=؟؟​

Answers

Alright idk y u said that here but ok

U
14 poi
At the college football game there were 48,000 people. If 77% of the
people at the game were supporters for the home team, how many
people were supporting the home team? *

Answers

Answer:

36960 people

Step-by-step explanation:

Answer:

36,960 people

Step-by-step explanation:

[tex]\frac{is}{of}=\frac{percent}{100}[/tex] is the formula to solve for this equation, here plugging in all our numbers gives us [tex]\frac{x}{480,000} = \frac{77}{100}[/tex].

We do not know our "is" so we replace it for x and solve → [tex]x=(480,000)(\frac{77}{100} )[/tex] = 36,960 people

Pete's checking account showed a balance at the beginning of the month of $180. After 3 days the checking account showed a balance of $160. Write a linear equations to represent the total in the checking account f(x) according to the day x.

Answers

Answer:

180 - 172 =$8 8/3=2.56

A 95​% confidence interval of 17.6 months to 49.2 months has been found for the mean duration of​ imprisonment, mu​, of political prisoners of a certain country with chronic PTSD. a. Determine the margin of​ error, E. b. Explain the meaning of E in this context in terms of the accuracy of the estimate. c. Find the sample size required to have a margin of error of 11 months and a 99​% confidence level.​ (Use sigmaequals45 ​months.) d. Find a 99​% confidence interval for the mean duration of​ imprisonment, mu​, if a sample of the size determined in part​ (c) has a mean of 36.5 months.

Answers

Answer:

a) [tex] E = \frac{49.2-17.6}{2}= 15.8[/tex]

b) For this case we have 95% of confidence that the true mean would be between [tex]\pm 15.8[/tex] units respect the true mean.

c) [tex]n=(\frac{2.58(45)}{11})^2 =111.39 \approx 112[/tex]

So the answer for this case would be n=112

d) [tex]36.5-2.58\frac{45}{\sqrt{112}}=25.53[/tex]    

[tex]36.5+2.58\frac{45}{\sqrt{112}}=47.47[/tex]

Step-by-step explanation:

Part a

For this case we know that the cinfidence interval for the true mean is given by:

[tex] \bar X \pm E[/tex]

Where E represent the margin of error. For this case we have the confidence interval at 95% of confidence and we can estimate the margin of error like this:

[tex] E = \frac{49.2-17.6}{2}= 15.8[/tex]

Part b

For this case we have 95% of confidence that the true mean would be between [tex]\pm 15.8[/tex] units respect the true mean.

Part c

The margin of error is given by this formula:

[tex] ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]    (a)

And on this case we have that ME =11 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

[tex]n=(\frac{z_{\alpha/2} \sigma}{ME})^2[/tex]   (b)

The critical value for 99% of confidence interval now can be founded using the normal distribution. The critical value would be [tex]z_{\alpha/2}=2.58[/tex], replacing into formula (b) we got:

[tex]n=(\frac{2.58(45)}{11})^2 =111.39 \approx 112[/tex]

So the answer for this case would be n=112

Part d

The confidence interval for the mean is given by the following formula:

[tex]\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]   (1)

Replcaing the info given we got:

[tex]36.5-2.58\frac{45}{\sqrt{112}}=25.53[/tex]    

[tex]36.5+2.58\frac{45}{\sqrt{112}}=47.47[/tex]

Factor the expression. d2 + 12d+ 36

Answers

Answer:

the factored expression is

(d+6)(d+6) or (d+6)^2

Step-by-step explanation:

Pls help with this one I will give brainliest thank you!

Answers

Answer:

B. 10 in.

Step-by-step explanation:

When you do length times width times height 10*10*10 equals 1000

10*10=100 and 100*10=1000

Answer:10 feet

Step-by-step explanation:

edge=[tex]\sqrt[3]{1000}[/tex]= 10 so the answer is B

HELP ME ASAP! Will give BRAINLIEST! Please read the question THEN answer correctly! No guessing.

Answers

Answer:

In this case, you should check the x-intercept (y = 0).

=> (x-3)(x+4) = 0

=> Two x-intercept at x = 3 and x = -4

C, D are  not right, because there is no two x-intercepts.

A is not correct, because both of x-intercepts are less than 0.

=> Option B is correct.

Hope this helps!

:)

Math Help!!! Can someone solve this?? I will give you Brainliest!!!!!!

Answers

Answer:first one is false, second is true and third is true

Step-by-step explanation:

Audrey collected 4⁄5 pint of blueberries. Addison collected 12 times as many pints of blueberries as Audrey. How many pints of blueberries did Addison collect?

Answers

Answer:

48/5≈ 9 3/5

Step-by-step explanation:

12 is the same thing as 12/1

so your multiply fractions

4/5 times 12/1

numerator=top

denominator=bottom

so to multiply a fraction you multiply the numerator times the numerator

so in that case your multiplying 4 times 12

=48

to find the bottom half you multiply the denominator times the denominator

in that case is 5 times 1

=5

numerator/denominator

48/5

if you want to simplify it further simply divide 48/5

5 goes into 48 about 9 times

and were left with 3/5

so 9 and 3/5

pls mark me brainliest

Find the ratio a:b, if it is given that ...
7a=3b

Answers

Answer:

a:b

3:7

Step-by-step explanation:

a:b  also means a/b

Taking the equation

7a = 3b

Dividing each side by b

7a/b = 3b/b

7 a/b = 3

Divide each side by 7

a/b = 3/7

The ratio is 3/7

a:b

3:7

Answer:

a:b = 3/7

Step-by-step explanation:

we need to find the ratio a:b which is the same as a/b.

7a=3b

Devide left and right of the = sign by b gives

7a/b = 3 * b/b

7a/b = 3 * 1

7a/b = 3

Multiply left and right of the = sign by 1/7 gives

1/7 * 7a/b = 1/7 * 3

7/7 * a/b = 3/7

1 * a/b = 3/7

a/b = 3/7

Since a/b is the same as a:b, we now have the answer.

a:b = 3/7

help help help please

Answers

Answer:

to add to the table, continue the arithmetic sequence in each columnto use the table, extend the third column to 45, or multiply the first row by 9

Step-by-step explanation:

The numbers in the first column are an arithmetic sequence with a common difference of 2. The next few numbers will be 6, 8, 10, ...

The numbers in the second column are an arithmetic sequence with a common difference of 3. The next few numbers will be 9, 12, 15, ...

The numbers in the third column are an arithmetic sequence with a common difference of 5. The next few numbers will be 15, 20, 25, ...

To use the table, Mark can extend each sequence until he has a row with 45 in the third column, or he can multiply or add rows to give a result of 45 in the third column. For example, multiplying the first row by 9 gives 18:27:45 meaning that Mark needs 18 liters of blue and 27 liters of yellow to make 45 liters of green paint.

what is the result of 3×3/5×(-8×1/3)

Answers

Answer:

-4.8

Step-by-step explanation:

Answer:

−24/5

Step-by-step explanation:

3x3/5x(-8x1/3)

Use the order of operations method, PEMDAS, in order to solve this expression.

Fernanda is filling a cylindrical pot with cans of vegetable soup. The pot has a diameter of 15 in. and a height of 10 in. The soup can has a diameter of 4 in. and a height of 5 in. How many cans of soup will it take to fill up the pot?

Answers

Answer:

28.125 cans

Step-by-step explanation:

Step 1: Determine the Volume of the Pot

Diameter= 15 inches, therefore Radius=15/2=7.5 Inches

Height =10 Inch

Volume of a cylinder =[tex]\pi r^2h[/tex]

Volume of the Pot [tex]=\pi*7.5^2*10=562.5\pi[/tex] cubic inches.

Step 2: Determine the Volume of each can

Diameter= 4 inch, therefore Radius=4/2=2 Inches

Height =5 In.

Volume of a cylinder =[tex]\pi r^2h[/tex]

Volume of one can [tex]=\pi*2^2*5=20\pi[/tex] cubic inches.

Step 3: Divide the Volume of the Pot by the Volume of the can

To obtain the number of cans that will fill the pot, we divide the Volume of the Pot by the Volume of the can.

Volume of the Pot÷Volume of one can

[tex]=562.5\pi \div 20\pi\\=28.125 \:cans[/tex]

Therefore, we conclude that it takes 28.125 cans to fill up the cylindrical pot of soup.

given h(x)=-2x+5, find h(-6)

Answers

This question is easy! it's simply asking to plug in -6 instead of the variable x.

h(-6)=-2(-6)+5

       =12+5

       =17

17 is your final answer.

:
What is 475.189 rounded to the nearest hundredth?

Answers

Answer:

It is:475.19.

HOPE THIS HELPED

Answer:

475.19.

Step-by-step explanation:

The hundredths place is two places to the right of the decimal, or (0.01).

In the number given, the number to the right of the hundredths place is larger than 5, meaning we will round up giving us:

475.189 --> 475.19.

Write the slope-intercept form of the equation of the line through (-1,4) and parallel to x=5

Answers

Answer:

x = -1

Step-by-step explanation:

When lines are parallel, they have the same slope

x = 5 means the line is a vertical line going through x=5

The new line is a vertical line

We have a point (-1,4)

It will need to go through the x point of -1 and be a vertical line ( which is in the form x=  )

x=-1

Not sure on how to do these questions

Answers

Answer:f(8)=g(8)

Step-by-step explanation:

So in these problems f(8) means that you look at the f(x) function (function 1) and plug in 8 for x.  Then since it says g(8), you look at the g(x) function and substitute x for 8.  If we do that, f(x)=2(8)-3 which is 13.  g(x)=3/2x+1=13.  The two of them are equal when x=8.  So the answer is the third choice

Answer:

f(8)=g(8)

Step-by-step explanation:

Just put the values of given functions in the equation

What is the length of AC?

Answers

Answer:

2.96

Step-by-step explanation:

The cosine of an angle is the length of the adjacent side divided by the length of the hypotenuse. In this case:

[tex]\cos 65=\dfrac{x}{7}[/tex]

[tex]x=7\cdot \cos 65\approx 2.96[/tex]

Hope this helps!

Northlake high scores to lunch. Soon can eat their lunch in the cafeteria or on an outside patio about 35% of students who have first lunch eat outside compare this with a percenta

Answers

Answer:

The proportion of second lunch students who eat outside is more than that for the first lunch students.

Step-by-step explanation:

The complete question is:

Points Northlake High School has two lunch periods. Students can eat their lunch in the cafeteria or on an outside patio. About 35% of students who have first lunch eat outside. Compare this with the percentage of second-lunch students who eat outside.

                            Eat Outside         Eat Inside          Total

First Lunch                 0.19                    0.35               0.54

Second Lunch           0.22                   0.24               0.46

Total                           0.41                    0.59               1.00

Solution:

The conditional probability of an event B given that another event A has already occurred is:

[tex]P(B|A)=\frac{P(A\cap B)}{P(A)}[/tex]

The probability of students who have second lunch (S) and eat outside (O) is:

P (S ∩ O) = 0.22

The probability of students who have second lunch (S) is:

P (S) = 0.41

Compute the proportion of student who eats outside given they have second lunch as follows:

[tex]P(O|S)=\frac{P(S\cap O)}{P(S)}[/tex]

            [tex]=\frac{0.22}{0.41}\\\\=0.536583\\\\\approx 0.54[/tex]

The proportion of second lunch students who eat outside is more than that for the first lunch students.

What’s the correct answer for this?

Answers

Letter C because it is being reflected over the x axis and having a translation through the horizontal line

Answer:

C.

Step-by-step explanation:

A reflection across a horizontal line will move the quadrilateral downwards and opposite and then a horizontal translation will move the quad on to the other quad and thus it will be proved that both quads are congruent

Graphs of what functions are shown below?

Answers

Answer:

 y = -√(x -5) +2

Step-by-step explanation:

This looks like a square root function reflected vertically, and translated up 2 and right 5.

 y = -√(x -5) +2

_____

g(x) = a·f(x -h) +k   represents a translation of f(x) by (h, k) and a vertical scaling by a factor of "a". If "a" is negative, the function is reflected across the x-axis.

. The pet store salesman told Evan to feed his dog 8 ounces of food per day. The food is sold in pounds. How many pounds does Evan need to buy for 2 weeks of feeding his dog? (16 ounces = 1 pound)?

Answers

It’s 7 pounds. 8 ounces per day then multiply that by 7 days which is 56 ounces then multiply 56 by 2 which makes 112, then multiply 112 by 16 which stands for ounces and you get 7.

An elementary ntimesn scaling matrix with k on the diagonal is the same as the ntimesn identity matrix with _______ exactly one at least one all of the ______ 0's 1's replaced with some number k. This means it is _______ an invertible matrix, a zero matrix, a singular matrix, a triangular matrix, an identity matrix, and so its determinant is the _______ sum product of its diagonal entries.​ Thus, the determinant of an elementary scaling matrix with k on the diagonal is nothing.

Answers

Answer:

exactly one, 0's, triangular matrix, product and 1.

Step-by-step explanation:

So, let us first fill in the gap in the question below. Note that the capitalized words are the words to be filled in the gap and the ones in brackets too.

"An elementary ntimesn scaling matrix with k on the diagonal is the same as the ntimesn identity matrix with EXACTLY ONE of the (0's) replaced with some number k. This means it is TRIANGULAR MATRIX, and so its determinant is the PRODUCT of its diagonal entries.​ Thus, the determinant of an elementary scaling matrix with k on the diagonal is (1).

Here, one of the zeros in the identity matrix will surely be replaced by one. That is to say, the determinants = 1 × 1 × 1 => 1. Thus, it is a a triangular matrix.

word problem of addition or subtraction

Answers

Answer:

subtraction

Step-by-step explanation:

In order to find out how many more flowers you need, you need to subtract both of the numbers to get the difference.

Answer:19

Step-by-step explanation:subtract 27 from 8.

I keep gettin it wrong please help!!!

Answers

Answer:

-5≤ x ≤5 or [-5,5]

Step-by-step explanation:

domain is related to independent variable x

black dots means that number is included in the domain

in this case function is from -5,5 included or -5≤ x ≤5 or [-5,5]

НА
.
-
НА
N
1 point
Which has a value 10 times greater than 0.008?
о 0.8
o0.08
ов
а
3
80

Answers

????????????????????

five more than the quotient of y and 2 is -3

Answers

Answer:

y/2 + 5 = -3

y/2 = -8

y = -16

Step-by-step explanation:

A circle has a circumference that is greater than 8 meters. The inequality 3.14 d greater-than 8 can be used to determine the possible lengths of the diameter of the circle. What are the possible values of d, the length of the diameter in meters?
d less-than 25.1
d greater-than 25.1
d less-than 2.5
d greater-than 2.5

Answers

Answer:

It is the last one

Step-by-step explanation:

Answer:

it is d

Step-by-step explanation:

Two datasets arranged in descending order are; {8, x, 4,1} and {9, y, 5,2}. If the medians of
the two given datasets are equal, what is the value of (y − x)
2
?

Answers

Answer:

1

Step-by-step explanation:

A data arranged in descending order is a data arranged from the biggest to the smallest. The medisn of the data sets is the value at the middle of the dataset after rearrangment.

For the dataset {8, x, 4,1}, the median will be x and 4. Since we have two median values, we will take their average as shown

Median(1) = [tex]\frac{x+4}{2}[/tex]... 1

Simialrly for dataset {9, y, 5,2}, the median will be y and 5.

Median(2) = [tex]\frac{y+5}{2}[/tex] ...2

Since the medians of  the two given datasets are equal, we will equate equation 1 and 2 and calculate for y-x as shown;

[tex]\frac{x+4}{2} = \frac{y+5}{2}[/tex]

[tex]x+4 = y+5\\x-y = 5-4\\x-y = 1\\y-x = -1[/tex]

Therefore y-x = -1

(y-x)² = (-1)²

= 1

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