1.Use the Z-score applet from the website below to do the following problem. Pro
ID: 3306085 • Letter: 1
Question
1.Use the Z-score applet from the website below to do the following problem. Provide a screen shot for your answers.
http://davidmlane.com/hyperstat/z_table.html
The average punt in football travels 40 yards from the line of scrimmage. The standard deviation is 5 yards. Assume that the distance distribution follows the Bell curve. Provide screen shots of your answers.
a.If a punt travels a distance of 50 yards, what percentile is it in? (use “Area from a value”)
b.If a punt is in the 85th percentile, how far did the football travel? (use “Value from an area”)
What is the z-score of a punt of 37 yards? (z c.Explanation / Answer
1.
Mean ( u ) =40
Standard Deviation ( sd )=5
Normal Distribution = Z= X- u / sd ~ N(0,1)
a.
P(X < 50) = (50-40)/5
= 10/5= 2
= P ( Z <2) From Standard Normal Table
= 0.9772
P(X > = 50) = (1 - P(X < 50)
= 1 - 0.9772 = 0.0228
= 2.28%
b.
P ( Z < x ) = 0.85
Value of z to the cumulative probability of 0.85 from normal table is 1.036
P( x-u/s.d < x - 40/5 ) = 0.85
That is, ( x - 40/5 ) = 1.04
--> x = 1.04 * 5 + 40 = 45.1822
c.
P(X < 37) = (37-40)/5
= -3/5= -0.6
= P ( Z <-0.6) From Standard Normal Table
= 0.2743
P(X > = 37) = (1 - P(X < 37)
= 1 - 0.2743 = 0.7257
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