# Wk 5 Word Problem Exercise

**Topics:**Normal distribution, Sample size, Standard deviation

**Pages:**2 (300 words)

**Published:**January 14, 2013

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PLEASE DO NOT USE ANY RED FONTS

#1 Find the standard error of the mean for each sampling situation (assuming a normal population). What happens to the standard error each time you quadruple the sample size? a. σ = 36, n = 9 36

√9=12

b. σ = 36, n = 36 36

√36=6

c. σ = 36, n = 144 =3

formula SE= σ

√n

#2. A sample was taken of 36 people attending a school with an annual average tuition of $3800 and the population standard deviation of $620. Find the 95% confidence interval of the true mean. 3,800+1.960 (620/√36) =4,002.5

3,800- 1.960 (620/√36)=3,597.5 I am 95% confident the # is between 4,002.5 and 3,597.5 _

formula CI= X + Z(s/√n

#3 A sample of 25 bank loan customers showed initial application times to have a mean of 22.55 minutes and a standard deviation of 3.8minutes. A) Find a 99 percent confidence interval for μ, assuming that the sample is from a normal population. B) How could the confidence interval be made narrower? 22.55+2.576 (3.8/√25)= 24.50

22.55- 2.576 (3.8/√250=20.60 I am 99% confident the #is between 24.50 and 20.60 _

Formula CI= X + Z(s/√n

#4 A prior study showed that the average ATM cash deposit took 60 seconds with a standard deviation of 12 seconds. The study is to be repeated this year. How large a sample would be needed to estimate this year’s mean with 99 percent confidence and an error of + or - 2 seconds? 60+2.576 (12)

60-2.576(12

√2 =81.9

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