Question

given a normal distribution with mean =50 and standard deviations =10 find the value of X that has
1. 13% of the area to its left and
2. 14%. of the area to its right​

Answer 1

Given :  given a normal distribution with mean =50 and standard deviations =10

To find : the value of X that has

1. 13% of the area to its left and

2. 14%. of the area to its right​

Solution:

Mean = 50

SD = 10

Value = X

Z score = ( Value - Mean) /SD

13% of the area to its left = 0.13

=>  Z score =  - 3

-3 = (X - 50)/10

=> -30 = X  - 50

=> X = 20

the value of X  20  has  13% of the area to its left  

14%. of the area to its right​ =0.14

1 -0.14 = 0.86

=> Z score = 1.08

1.08 = ( X - 50)/10

=> X = 60.8

the value of X  60.8  has  14%. of the area to its right​

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