Question

Probability that a randomly selected student will weigh less than 140 lbs=0.2451

Probability that a randomly selected student will weigh more than 190 lbs=0.1292

Probability that a randomly selected student will weigh between 150 & 180 lbs= 0.4057

Using the information above, assume that you are going to randomly sample n=10 students.

1) What is the probability that the average of the selected student will be less than 140 lbs?

2) What is the probability that the average of the selected student will be more than 190 lbs?

3) What is the probability that the average of the selected student is between 150 & 180 lbs?

Answer 1

Let X denotes the weight of a randomly selected student.

Given

... (1)

Moreover,

... (2)

Substracting equation (2) from equation (1), we get

From equation (2), we have

Now, X ~ Normal(162.53, 27.4699²)

Let denotes the sample mean of a sample of size 10

So, or

1. The probability that the average of the selected student will be less than 140 lbs

2. The probability that the average of the selected student will be more than 190 lbs

3. The probability that the average of the selected student is between 150 & 180 lbs

(ans)