1.Use the Z-score applet from the website below to do the following problem. Pro

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”)

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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