Posted by **harish** on Wednesday, February 13, 2013 at 7:11am.

the heights of female students at a particular college are normally distributed with the mean 169 cm and standard deviation 9 cm.

1) Given that 80% of these female students have a height less than h cm ,find the value of h.

2) Given that 60% of these female students have a height greater than s cm,find the value of s.

- maths -
**Deminic**, Sunday, November 29, 2015 at 12:00pm
0.7

- statistics -
**lilian**, Friday, February 12, 2016 at 5:02am
1) H~N(169,9^2)

(H<h)=0.80

(H< (h-169)/9)=0.80

(H<a)=0.80

(fi)a =0.80 (look for 0.80 in the normal distribution table)

the closest # to 0.80 is 0.7995 at 0.84

0.0005 is left to make 0.80 so look for that in the add part of the table 5 is at 2

so the a=0.842

we suggested a as (h-169)/9 =0.842

solve, h=176.6

2) (H>s)=0.6

Standardize the s , (H>(s-169)/9)=0.6

(H>b)=0.6

s is negative because ; if its greater than the random variable which is (s) and the probability is greater than 0.5 then the random variable is negative

rule states that ; (fi)b=0.6

from the table (0.6) is 0.5987 at 0.25

0.0013 left for it to equal 0.6

from the table take the minimum value which is 12 at 3

so b is 0.253

its ngative so b is -0.253

(s-169)/9=-0.253

s=166.7

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