If X follows normal distribution with mean 120 and standard deviation

1.	If X follows normal distribution with mean 120 and standard deviation 40, the p(X
Answer» $\large\underline{\sf{Solution-}}$ 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.