Question

The weights of a women population are normally distributed with mean 60kg and standard deviation 5kg. Find the probability that the weight of a woman chosen at random is more than

65kg.

Answer 1

To determine the probability of making options from random choices, the following expression is utilized: $X-N\left(\mu ,\:\sigma ^2\right)\:hence\:Z=\frac{X-u}{\sigma }-N\left(0,\:1\right)$ provided that weight$W-N\left(60,\:5^2\right)$ then $Z=\frac{W-60}{5}-N\left(0,\:1\right)\:$

To calculate $P\left(W>65\right)$

$P\left(W>65\right)\:=P\left(\frac{W-60}{5}>\frac{65-60}{5}\right)$

$=P\left(Z>1\right)$

$=1-0.9772$

$=0.0228\:$