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Textbook Illowsky            Page 406              Problem 96 

Xbar is notation for average .

Excel  =NORM.DIST()

A typical adult has an average IQ score of 105 with a standard deviation of 20. 

If twenty (25) randomly selected adults are given an IQ test:

a     What is the probability that the sample mean (xbar) scores will be equal to or less than 100 points?

Find the probability that P( Xbar =< 100 )

Enter answer rounded to 2 decimal places.

Include a 0 to the left of the decimal point if your answer is less than 1.

Do not enter answer as a percent.

________

b     What is the probability that the sample mean scores will be between 100 and 115 points?

Find the probability that P(100 <= X =< 115) 

Enter answer rounded to 3 decimal places with a 0 to the left of the decimal point.

Do not enter answer as a percent.

________

Textbook Illowsky            Page 400              Problem 62

http://stattrek.com/online-calculator/normal.aspx 

Excel
           =NORM.DIST()
           =NORM.INV()

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 250 feet and a standard deviation of 50 feet. We randomly sample 49 fly balls.

X ¯   is notation for the average value of the x's.

If X ¯ = average distance in feet for 49 fly balls, then X ¯ ~ _______(_______,_______)

For the following three blanks fill in the correct answers.

For blank 1 Select the appropriate distribution by entering the corresponding letter.

a      Normal Population Distribution (parent)

b      Normal Sampling Distribution

______

For blank 2 What is the numerical value of the mean( mu) ? Enter answer with 0 decimal precision (Integer).

______

For blank 3 What is the Standard Deviation of the Sampling Distribution?  (The standard error of the mean). Enter answer with 2 decimal place precision. 

______

What is the probability that the 49 balls traveled an average distance of less than 240 feet? 
 

The P(X ¯ < 240) =

Enter answer to 3 decimal place precision.

Do not enter answer as a percent. Include a 0 to the left of the decimal point.  

________

Find the 80th percentile of the Sampling Distribution of Averages for the average of the 49 fly balls.

Find the X ¯ value such that P(X < X ¯) = .80

Enter answer to 1 decimal place precision.