standard normal distribution/ PLEASE HELP

[agirl]

I have this question: Men are eligible for this club if they are 74in tall. what percentage of men are eligible to join the club. also the mean of men with normally distributed heights are 69.0in and the standard deviation is 2.8in

could someone help me with this please!

 

[vinayan]

Here to find P[X>74] where X has normal distribution with mean 69 and standard deviation 2.8. Multiply the result with 100 to obtain the % of men.

 

[NnmB35]

mean = 69. sd = 2.8. % > 74. Find the z value to correspond to 74 in this scenario.
z = (x - mean)/sd
= (74 - 69)/2.8
= 5/2.8
= 1.79.
% corresponding to z = 1.79 = 0.4633.
This value is for the area of the graph between the mean (69) and the value of X (I used the table for Areas under the graph). To calculate the value for >74, 0.5 - 0.4633 = 0.0367. So 3.67% of men would fit the criteria of being 74" or taller. (I won't qualify for the group!)