If X is normally distributed with mean 10 and standard deviation 4, find x such that the probability of X between 10 and x is 0.4772.

18

The correct answer is Option (4) → 18

Given $μ = 10, σ = 4$.

Also, $P(10 < x < x) = 0.4772,$

then $Z =\frac{X-10}{4}$

$P(10 <X < x)= 0.4772$

$⇒P\left(\frac{10-10}{4}<Z<\frac{x-10}{4}\right)= 0.4772$

$⇒P\left(0 <Z<\frac{x-10}{4}\right)= 0.4772$

$⇒F\left(\frac{x-10}{4}\right)- F(0) = 0.4772$

$⇒F\left(\frac{x-10}{4}\right)-0.5= 0.4772$   (using property 2)

$⇒F\left(\frac{x-10}{4}\right)= 0.9772$

$⇒\frac{x-10}{4}=2$   (using table)

$⇒x = 18$