Answer to Question #99321 in Statistics and Probability for Douglas

Question

mean weight of 500 student in a certain school is 151pounds and standard deviation is 15 pounds. Assuming that the weights are normally distributed, find how many student weighs
(a) between 120 and 155pounds
(b)mord than 18.5 pounds

Answer 1

Given that $\mu=151,\sigma=15,n=500$

Let X be the random variable denoting the weight of the students.

a) Then we have to find $P(120<X<155)$

Let Z be the standard normal variable, then

$Z=(X-\mu)/\sigma$

When $X=120$

$Z=(120-151)/15$

$=-2.07$

When $X=155$

$Z=(155-151)/15$

$=0.27$

$P(120<X<155)=P(-2.07<Z<0.27)$

$=P(Z<0.27)-P(Z<-2.07)$

$=0.606-0.019=0.587$

Now the number of required student will be $(500*0.587)\approx244$

b)

We have to find $P(X>18.5)$

Let Z be the standard normal variable, then

$Z=(X-\mu)/\sigma$

When $X=18.5$

$Z=(18.5-151)/15$

$=-8.83$

$P(X>18.83)=P(Z>-8.83)$

$=1-P(Z<-8.83)$

$\approx1$

Now the number of required student will be $(500*1)=500$