Cellular phone bills for residents of a city have a mean of $63 and a standard d

Question

Cellular phone bills for residents of a city have a mean of $63 and a standard deviation of $11. Random samples of 100 cellular phone bills are drawn from this population and the mean of each sample is determined. Find the mean and standard error of the mean of the sampling distribution a. mean 1. b. standard error of the mean 2. An education finance corporation claims that the average credit card debts carried by undergraduates are normally distributed, with a mean of $3173 and a standard deviation of $1120. You randomly select 25 undergraduates who are credit card holders. What is the probability that their mean credit card balance is less than $2700? 3. Fora sample of n 46, find the probability of a sample mean being less than 23.3 if the population mean is 24 and population standard deviation is 1.25 , 186 233 Determine whether the statement is true or false. If it is false, rewrite it as a true statement. 4. As the size of a sample increases, the mean of the distribution of sample means increases

Explanation / Answer

1. Mean is same as 63

standard erorr SE=s/sqrt(N)=11/sqrt(100)=1.1

2. mean is 3173 and s is 1120

for sample size of 25, the standard error is s/sqrt(N)=1120/sqrt(25)=224

z is (xbar-mean)/SE

P(xbar<2700)=P(z<(2700-3173)/224)=P(z<-2.11) or 1-P(z<2.11)

from normal distribution table we get 1-0.9826=0.0174

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