Answer to Question #320777 in Statistics and Probability for Fayneath Merrie Bu

Question

The 1500 students weight are normally distributed with a mean of 50kg with the standard deviation of S-5 lbs?

A. How many students are less than 46kg

B. How many students are heavier than 113.5lbs

Answer 1

1 pound is equal to 0,4536 kilograms.

We have a normal distribution,

$\mu=50 \textnormal{ kg}=\cfrac{50}{0.4536}=110.2 \textnormal{ lbs}, \\ \sigma=5 \textnormal{ lbs}=5\cdot0.4536=2.27\textnormal{ kg}.$

Let's convert it to the standard normal distribution, $z=\cfrac{x-\mu}{\sigma}.$

A. The probability that the student is less than 46kg:

$z_1=\cfrac{46-50}{2.27}=-1.76,$

$P(X<360\textnormal{ kg})=P(Z<-1.76)=0.0392$ ​(from z-table).

The number of such students:

$0.0392\cdot1500=58.8\approx59.$

B. The probability that the student is heavier than 113.5 lbs:

$z_2=\cfrac{113.5-110.2}{5}=0.66,$

$P(X>113.5\textnormal{ lbs})=P(Z>0.66)=1-P(Z<0.66)=\\ =1-0.7454=0.2546$

​(from z-table).

The number of such students:

$0.2546\cdot1500=381.9\approx382.$