Question

Suppose the variable x is represented by a standard normal distribution. What value of x is at the 40th percentile of the distribution

Answer 1

The value value of x is at the 40th percentile of the distribution is 0.65.

The standard normal distribution is a normal distribution with a mean of zero and standard deviation of 1. The standard normal distribution is centered at zero and the degree to which a given measurement deviates from the mean is given by the standard deviation

Given:- μ$_X$=0,σ$_X$=1

We can standardize the random variable: Z=(X−μx)/σx,

Then the equation is P(X≤ x )=Φ(x−μx/σx)=Φ(x−0/1)=0.4

Inverse function

Ф$\\^{-1}$(0.4) = $\frac{x-0}{1}$

From the table we get,

Ф$^{-1}$ = 0.65

Thus

$\frac{x-40}{10}$ = 0.65

x -0 = 0.65

x = 6.5

Thus the value value of x is at the 40th percentile of the distribution is 0.65

Learn more about standard normal distribution here :

https://brainly.com/question/25394084

#SPJ4