We have 95 students in a class. Their abilities/eagerness are uniform randomly distributed on a scale...

We have 95 students in a class. Their abilities/eagerness are uniform randomly distributed on a scale between 1 and 4; and at the end of the class they will be judged right and they will receive a grade corresponding to their ability/eagerness (corresponding to their performance). What is the probability that the class average will be between 2.8 and 4? How would this number change (if it does) for 120 students?

Solutions

Expert Solution

We are given the distribution for each student here as:

Therefore the mean and variance of this distribution is obtained here as:

Therefore for 95 students, the distribution for the sample mean is given as: (Using Central limit theorem)

The probability here is computed as:

Converting it to a standard normal variable, we get here:

Getting it from the standard normal tables, we get here:

Therefore 0.0004 is the required probability here.

For 120, students we get the sample size here as n = 120, therefore we get here:

Getting it from the standard normal tables, we get here:

Therefore 0.0001 is the required probability here.

milcah answered 2 weeks ago

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