Question

QUESTION 1

1. Which of the following would probably be a normal distribution with a positive skew? Check all that apply.

   		Housing prices
   		Visits to the dentist in the past year
   		Height
   		Cigarettes smoked per day (in a county where most people don't smoke)

20 points   

QUESTION 2

1. What portion of a standard normal distribution is less than 1.5 standard deviations above the mean? (Express your answer as a number between zero and one, rounded to four decimal places.)

10 points   

QUESTION 3

1. What portion of a standard normal distribution is less than 1.5 standard deviations above the mean andmore than 1.5 standard deviations below the mean? (Express your answer as a number between zero and one, rounded to four decimal places.)

10 points   

QUESTION 4

1. Carla's company makes water heaters. These heaters last an average of 60 months, with a standard deviation of 8 months, before needing to be serviced. Her accountants estimate that the company can afford to replace 10% of all water heaters and still make a tidy profit.

   Rounding to the nearest whole number, how many months should the warranty be?

20 points   

QUESTION 5

1. If the margin of error for a confidence interval is 50 and the sample average is 160, what is the lower bound of the confidence interval?

5 points   

QUESTION 6

1. If the margin of error for a confidence interval is 50 and the sample average is 160, what is the upper bound of the confidence interval?

5 points   

QUESTION 7

1. Suppose you're estimating how much cloth you'll need to make a costume. If the margin of error of your confidence interval is 0.8 yards, what's the range of your confidence interval?

10 points   

QUESTION 8

1. Suppose you want to estimate the sales per customer for the next holiday season. Based on past seasons, the population standard deviation is $60. Based on a survey sample of 36 people, you estimate this season each customer will spend an average of $900. At 95% confidence, what is the margin of error? Do not include a dollar sign ($) in your answer.

Answer 1

2)

P(Z ≤   1.50   ) =   0.9332   (answer)
excel formula for probability from z score is =NORMSDIST(Z)

3)

P (    -1.500   < Z <    1.500   )                       
= P ( Z <    1.500   ) - P ( Z <   -1.50   ) =    0.9332   -    0.0668   =    0.8664   (answer)

4)

µ=   60                  
σ =    8                  
P(X≤x) =   0.9000                  
                      
Z value at    0.9   =   1.2816   (excel formula =NORMSINV(   0.9   ) )
z=(x-µ)/σ                      
so, X=zσ+µ=   1.282   *   8   +   60  
X   =   70.25   (answer)          

5) lower bounds = sample mean - margin of error = 160-50 = 110

6) upper bounds = sample mean + margin of error = 160+50 = 210

7) range = 2*0.8 = 1.6

8)

Level of Significance ,    α =    0.05          
'   '   '          
z value=   z α/2=   1.960   [Excel formula =NORMSINV(α/2) ]      
                  
Standard Error , SE = σ/√n =   60.0000   / √   36   =   10.0000
margin of error, E=Z*SE =   1.9600   *   10.0000   =   19.60