The amount people pay 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.

Part B: What is the shape of the sampling distribution of x?? Justify your answer.

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. 

Answer:

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

• x? = $142
• ?σx??? = 0.749

Part B: What is the shape of the sampling distribution of x??

• The form of the sampling distribution of x?, using the central limit theorem, the sampling distribution can be approximately normal by: N(?μ? ,?σx??? )

Part C: What is the probability that the average cable service paid by the sample of cable service customers will exceed $143?

• P(x? > 143) = 0.0901

Step-by-step explanation

Data:

The amount people pay for cable service varies quite a bit, but the mean monthly fee is $142 and the standard deviation is $29. 

• ?μ=? $142
• ?σ=? $29

A sample survey is designed to ask a simple random sample of 1,500 cable service customers how much they pay.

• n = 1500

Let x? be the mean amount paid.

Solution:

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

the mean of the sample distribution is equal to the mean of the population ?μ=? $142

• x? = $142

To find the standard deviation of the sampling distribution of x?, the following formula is used

• ?σx??? = ??σ/n1/2??
• ?σx??? = ?29/?1500 1/2?? replacing data
• ?σx??? = 0.749

Part B: What is the shape of the sampling distribution of x??

• The form of the sampling distribution of x?, using the central limit theorem, the sampling distribution can be approximately normal by: N(?μ? ,?σx??? )
• for ?μ=? 142 and ?σx??? = 0.749
• N(142, 0.749 )

Part C: What is the probability that the average cable service paid by the sample of cable service customers will exceed $143?

• x? > 143 the average cable service paid by the sample of cable service customers will exceed $143
• P(x? > 143) = 1 - P(x? <143) complement probability
• formula for the standardization of x? for N(142, 0.749 )
• z =?x?−μ/ ?σx???
• for x = 143, z = ?143−142?/0.749? = 1.34 replacing data
• P(x? <143) = P(Z < 1.34) = 0.9099 using http://www.z-table.com (value 0.9099 is found in row 1.3 and column 0.04)
• P(x? > 143) = 1 - P(x? <143) = 1 - 0.9099
• P(x? > 143) = 0.0901

please use this google drive link to download the answer file.

https://drive.google.com/file/d/1k3rsgQFZC833wFSvM_5muSu4O2zCXvf7/view?usp=sharing

note: if you have any trouble in viewing/downloading the answer from the given link, please use this below guide to understand the whole process.

https://helpinhomework.org/blog/how-to-obtain-answer-through-google-drive-link