In a survey of men aged 20-29 in a certain country, the mean height is 73.4 inches with a standard deviation of 2.7 inches. Find the minimum height in the top 15% of heights.
Solution:
Given: Men aged 20-29 in a certain country, the mean height is 73.4 inches with a standard deviation of 2.7 inches.
Lets assume X follows a Normal distribution with mean= 73.4 inches and a standard deviation 2.7 inches.
We have to find : the minimum height in the top 15% of heights.
That is find x value such that:
P( X > x ) =15%
P( X > x ) =0.1500
thus we can write this as:
P( X < x ) =1 - P( X > x)
P( X < x ) =1 - 0.1500
P( X < x ) = 0.8500
That means: if area above x is 15% then area below x is 85%
Now use following steps in TI 84 plus calculator:
1) Press 2ND and press VARS
2) Select invNorma(
Enter Numbers:
for area we use left area , so we enter 0.8500 area.
Mean = 73.4
Standard deviation = 2.7
Click on Paste and press ENTER two times
Thus we get:
x = 76.19837
x = 76.2
Thus the minimum height in the top 15% of heights is x = 76.2 inches.
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