Question

In a normal distribution of large group of men 5% under 60 cm height and 40% are between 60 and 65. Find mean height and standard deviation?

Answer 1

Answer:

Step-by-step explanation:

In a normal distribution of large group of men 5% under 60 cm height and 40% are between 60 and 65.

Mean = 65.429

Standard deviation = 3.3

Answer 2

Given :  Of a large group of men,

5% are under 60 cm and

40% are between 60  and 65 cm

A normal distribution

To find :  the mean height and standard deviation.

Solution:

5% are under 60 cm  

40% are between  60  and 65 cm

=> 5 + 40 = 45 % under 65 cm

Mean = M  inches

SD = S   inches  ( SD = Standard Deviation )

Z score = ( Value - Mean)/SD

5% are under 60 cm  

Z score for 5 % =  -2.575

-2.575 = ( 60 - M)/SD

45 % under 65 cm

Z score for 45 % =  -0.125

-0.125 = ( 65 - M)/SD

20.6  = (60 - M)/(65 - M)

=> 1339 - 20.6M = 60 - M

=> 19.6M = 1281

=> M = 65.255

Substituting in any one

S = 2.041

Mean height = 65.255 cm

SD = 2.041 cm

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