Question

If X follows normal distribution with mean 120 and standard deviation 40, the p(X<140) is ___.Given that area between 0 and 0.5 is 0.1961. *

Answer 1

$\large\underline{\sf{Solution-}}$

Given that,

Mean of normal distribution = 120

$\rm :\longmapsto\: \mu \: = \: 120$

Standard deviation of normal distribution = 40

$\rm :\longmapsto\: \sigma \: = \: 40$

Let Z be a normal variable corresponding to X = 140, then

$\rm :\longmapsto\:Z = \dfrac{X - \mu}{ \sigma}$

$\rm :\longmapsto\:Z = \dfrac{140 - 120}{40}$

$\rm :\longmapsto\:Z = \dfrac{20}{40}$

$\bf\implies \:Z = 0.5$

Now,

We have to find P (X < 140),

$\rm :\longmapsto\:P(X < 140)$

$\: \: \rm = \: \: P(Z < 0.5)$

$\: \: \rm = \: \: 0.5 + P( 0 \leqslant Z \leqslant 0.5)$

$\: \: \rm = \: \: 0.5 + 0.1961$

$\: \: \rm = \: \: 0.6961$

Additional Information :-

1. In normal distribution, mean, median and mode are equal.

2. Area under the normal distribution curve is 1.

3. Normal distribution is symmetric about its mean.