Question

the weights of students in a junior college are normally distributed with a mean of 100 lbs. and a standard deviation of 18 lbs. What is the probability that a student drawn at random will weigh less than 150 lbs

Answer 1

Answer: 0.9973 .

Explanation:

Given: Weights of students in a junior college follows normal distribution with a mean = 100 lbs and a standard deviation =18 lbs.

Let X denotes the random variable that represents the weights of students .

Then, the probability that a student drawn at random will weigh less than 150 lbs will be :

`P(X<150)=P((X_\mu)/(\sigma)<(150-100)/(18))\\\\=P(Z<2.78 )\ \ \ \ [Z=(X_\mu)/(\sigma)]\\\\ =0.9973\ \ \ [\text{By p-value table for z}]`

Hence, the e=required probability is 0.9973 .