Answer to Question #345006 in Statistics and Probability for abby

Question

The weight (in kg) of grade 11 students in section Z follows a normal distribution with a mean 48 and a standard deviation of . Find the probability that students choosen at random has a weight less than 45

Answer 1

Let $X$ be random variable which defines weight of the students. In this problem we don't have standard deviation, so let it be 3, for example (you can substitute it for your standard deviation)

Then , $\mu =48$ and $\sigma =3$

Let us take $Z=\frac{X-\mu}{\sigma }$ . Then $Z=\frac{X-48}{3}$

(i) Probability that a student randomly selected is less than $45$ kg is $P(X<45)$ .

$\therefore P(X< 45)=P(Z < \frac{45-48}{3})$

$=P(Z < -1)$

$=0.1587$

(We found P using z-score table)