sample distribution

Question

Given X follows a N(mean= 40, standard deviation= 36) distribution, find the value of x that has 0.45 of
the area to the left. That is, find P(X less than or = x) = 0.45

Thanks in advance for your help

Answer 1

Hi JoAnna,

Standard normal distribution table lists the values of Z and the area under the curve.

Z = (x - 40)/36, P(X ≤ x) = 0.45 ,

P(X ≤ x) =P(Z ≤ (x - 40)/36)

From the standard normal distribution table, the closest value of the area to the left  

is 0.45 gives Z the value

Z = - 0.13 

(x - 40)/36 = - 0.13 

 x - 40 = - 4.68

 x = 35.32        

 

 

Answer 2

Try this, on TI-83 or TI-84 calculator, within the DISTR menu:

invnorm(0.45)

The answer you get is a Z-score:  -.12566. 

Now use the formula Z = (x - μ) / σ ... you know Z, μ and σ

and so you can solve for x, using basic Algebra.