Question

In: Statistics and Probability

Sampling Distribution. To commemorate Facebook’s 10-year milestone, Pew Research reported several facts about Facebook obtained from...

Sampling Distribution. To commemorate Facebook’s 10-year milestone, Pew Research reported several facts about Facebook obtained from its Internet Project survey. One was that the average adult user of Facebook has 338 friends. This population distribution takes only integer values, so it is certainly not Normal. It is also highly skewed to the right, with a reported median of 200 friends.

Suppose that σ = 380 and you take an SRS of 80 adult Facebook users.

a. For your sample, what are the mean and standard deviation of ̅ (xbar), the mean number of friends per adult user?

b. Use the central limit theorem to find the probability that the average number of friends for 80 Facebook users is greater than 350.

Solutions

Expert Solution

Answer:

Given that:

Suppose that σ = 380 and you take an SRS of 80 adult Facebook users.

(a) The mean of the sampling distribution of sample means is,



= 338
The mean of the sampling distribution of sample means is 338


The standard deviation of the sampling distribution of sample means is,
  

  

  

  


The standard deviation of the sampling distribution of sample means is 42.49

(b) The probability is that the average number of friends for 80 Facebook users is greater than 350 is,
First, compute the z score then find probability based on standard normal table.

For x =380 converts to

  

  

  


From the standard normal distribution table, the associated probability is 0.8389.

Since find the area to the right, so subtract from 1 to get,

P(z> 0.99) = 1 - (z <0.99)

= 1 - 0.8389

= 0.1611


The probability than is that the average number of friends for 80 Facebook users is greater than 350 is 0.1611.


Related Solutions

5.34 Number of friends on Facebook. To commemorate Facebook’s 10-year milestone, Pew Research reported several facts...
5.34 Number of friends on Facebook. To commemorate Facebook’s 10-year milestone, Pew Research reported several facts about Facebook obtained from its Internet Project survey. One was that the average adult user of Facebook has 338 friends. This population distribution takes only integer values, so it is certainly not Normal. It is also highly skewed to the right, with a reported median of 200 friends. 8 Suppose that σ = 380 and you take an SRS of 80 adult Facebook users....
A simple random sample of size 19 is obtained from a population that is normally distributed with a mean of 43,8 and a standard deviation of 2. Is the sampling distribution normally distributed? Why?
Which of the following is false? Correlation measures the strength of linear association between two numerical variables.  If the correlation between two variables is close to 0.01, then there is a very weak linear relation between them. Correlation coefficient and the slope always have the same sign (positive or negative). if the correlation coefficient is 1, then the slope must be 1 as well.A simple random sample of size 19 is obtained from a population that is normally distributed with a mean of 43,8...
On January 1, Year 1, Bryson Company obtained a $39,000, four-year, 10% installment note from Campbell...
On January 1, Year 1, Bryson Company obtained a $39,000, four-year, 10% installment note from Campbell Bank. The note requires annual payments of $12,303, beginning on December 31, Year 1. a. Prepare an amortization table for this installment note, similar to the one presented in Exhibit 4. Note: Round the computation of the interest expense to the nearest whole dollar. Enter all amounts as positive numbers. In Year 4, round the amount in the Decrease in Notes Payable column either...
On January 1, Gemstone Company obtained a $200,000, 10-year 9% installment note from Guarantee Bank. The...
On January 1, Gemstone Company obtained a $200,000, 10-year 9% installment note from Guarantee Bank. The note requires annual payments of $31,164, with the first payment occuring on the last day of the fiscal year. The first payment consists of interest of $18,000 and principal repayument of $13,164. The journal entry to record the payment of the first annual amount due on the note would include a Double-click on the box below to edit your answer choices. A.debit to cash...
10. A company reported annual sales revenue of $1,800,000. During the year, accounts receivable decreased from...
10. A company reported annual sales revenue of $1,800,000. During the year, accounts receivable decreased from a $56,000 beginning balance to a $48,000 ending balance. Accounts payable decreased from a $44,000 beginning balance to a $32,000 ending balance. How much is cash received from customers for this year? 11. A company reported annual sales revenue of $2,580,000. During the year accounts receivable increased from a $56,000 beginning balance to a $76,000 ending balance. Accounts payable decreased from a $52,000 beginning...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT