A university ed its applicants to write a short essay for its entra

Douglas Kraatz

Douglas Kraatz

Answered question

2021-12-02

A university asked its applicants to write a short essay for its entrance test. Based on their gathered data, it was found out that two out 10 students did not make grammatical mistakes, three out of 10 students made a grammatical mistake, four out of 10 students made two mistakes, and one out of 10 made three grammatical mistakes. What is the average number of grammatical mistakes made by the students in the essay?

Answer & Explanation

Otigh1979

Otigh1979

Beginner2021-12-03Added 17 answers

Step 1
For a set of random variables x1,x2,,xn corresponding probabilities of p1,p2,,pn, the mean is obtained as x=i=1nxipi.
For a set of random variables x1,x2,,xn corresponding probabilities of p1,p2,,pn, the variance is obtained as σ2=i=1nxi2pi(i=1nxipi)2.
Step 2
Consider that the random variable X defines the number of grammatical mistakes.
It is given that, two out 10 students did not make grammatical mistakes, three out of 10 students made a grammatical mistake, four out of 10 students made two mistakes, and one out of 10 made three grammatical mistakes.
Thus, X can take values 0,1, 2, and 3 with probabilities 210,310,410 and 110, respectively.
Consider the following table for necessary calculations.
xipixipi0210013100.324100.831100.3Total11.4
Thus, the mean is x=i=1nxipi=1.4.
Hence, the average number of grammatical mistakes made by the students in the essay is 1.4.

Do you have a similar question?

Recalculate according to your conditions!

New Questions in High school statistics

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?