Question

Suppose X~N(μ=1.5,σ=9). Find a number k such that P(X>k)=0.54. Round you answer to 3 decimal places.

Answer 1

Solution:-

Given that,

mean = = 1.5

standard deviation = = 9

Using standard normal table,

P(Z > z) = 0.54

= 1 - P(Z < z) = 0.54  

= P(Z < z) = 1 - 0.54

= P(Z < z ) = 0.46

= P(Z < -0.10 ) = 0.46  

z = -0.10 ( using z table )

Using z-score formula,

x = z * +

x = -0.10* 9+1.5

k=x = 0.6

P(X>0.6)=0.54