Mathematics : asked on ally7366
 06.08.2020

The amount people whopay for cable service varies quite a bit, but the mean monthly fee is $142 and the standard deviation is $29. The distribution is not

Normal. Many people pay about $76 for basic cable and about $160 for premium

service, but some pay much more. A sample survey is designed to ask a simple

random sample of 1,500 cable service customers how much they pay. Let X be the

mean amount paid.

Part A: What are the mean and standard deviation of the sample distribution of X?

Show your work and justify your reasoning. (4 points)

Part B: What is the shape of the sampling distribution of X? Justify your answer. (2

points)

Part C: What is the probability that the average cable service paid by the sample of

cable service customers will exceed $143? Show your work. (4 points) (10 points)

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Step-by-step answer

24.06.2023, solved by verified expert
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$142 ; 0.749 ; Normal ; 0.090938

Step-by-step explanation:

Mean and standard deviation :

The mean of the distribution x = $142, because the sample size is sufficiently large, the distribution will be approximately normal (central limit theorem).

Standard deviation of distribution : σ/ sqrt(n)

= 29 / sqrt(1500)

= 0.749

B.)

Shape of sampling distribution of X.

The shape of the sampling distribution will be approximately normal due to the large sample size used. This is according to the central limit theorem whereby distribution of sample converges to normal with increasing sample size. Mean ~ N(142, 0.749²)

C.)

P(X > 143)

Using the relation :

Z = (x - mean) / standard error

Z = 143 - 142) / 0.7489

Z = 1.335

P(Z > 1.335) :

Using the Z probability calculator :

P(Z > 1.335) = 0.090938

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Mathematics
Step-by-step answer
P Answered by PhD

$142 ; 0.749 ; Normal ; 0.090938

Step-by-step explanation:

Mean and standard deviation :

The mean of the distribution x = $142, because the sample size is sufficiently large, the distribution will be approximately normal (central limit theorem).

Standard deviation of distribution : σ/ sqrt(n)

= 29 / sqrt(1500)

= 0.749

B.)

Shape of sampling distribution of X.

The shape of the sampling distribution will be approximately normal due to the large sample size used. This is according to the central limit theorem whereby distribution of sample converges to normal with increasing sample size. Mean ~ N(142, 0.749²)

C.)

P(X > 143)

Using the relation :

Z = (x - mean) / standard error

Z = 143 - 142) / 0.7489

Z = 1.335

P(Z > 1.335) :

Using the Z probability calculator :

P(Z > 1.335) = 0.090938

Mathematics
Step-by-step answer
P Answered by PhD

SI=(P*R*T)/100

P=2000

R=1.5

T=6

SI=(2000*1.5*6)/100

=(2000*9)/100

=180

Neil will earn interest of 180

Mathematics
Step-by-step answer
P Answered by PhD

Cost of 7 gallons=$24.50

Cost of 1 gallon=24.50/7=3.5

Cost of 15 gallons=15*3.5=52.5

Cost of 15 gallons will be $52.5

Mathematics
Step-by-step answer
P Answered by PhD

For 1 flavor there are 9 topping

Therefore, for 5 different flavors there will be 5*9 choices

No of choices= 5*9

=45 

Mathematics
Step-by-step answer
P Answered by PhD

The answer is in the image 

The answer is in the image 
Mathematics
Step-by-step answer
P Answered by PhD

The solution is in the following image

The solution is in the following image
Mathematics
Step-by-step answer
P Answered by PhD

y=2x+15

where y=Value of coin

x=Age in years

Value of coin after 19 years=2*19+15

=$53

Therefore, Value after 19 years=$53

Mathematics
Step-by-step answer
P Answered by PhD

Salesperson will make 6% of 1800

=(6/100)*1800

=108

Salesperson will make $108 in $1800 sales

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