Question

7. Make up an application problem involving the normal distribution that includes three parts-one

dealing with the proportion or percent of data below a specified data value, one dealing with

the proportion or percent of data above a specified data value, and one dealing with the

proportion or percent of data between two specified data values.

Note :sometimes its hard to read thw writing !

Answer 1

7.

PROBLEM MAKE UP

Marks obtained by students of a class in STA2020 follows normal distribution with mean and standard deviation 72 and 18.5 respectively. Find the followings.

(a) What percent of students failed?

(b) What percent of students obtained A+ grade?

(c) What percent of students obtained B+ grade?

Grading system is as follows.

Grade	F (Fail)	C	C+	B	B+	A	A+
Marks	<35	35-45	46-55	56-70	71-80	81-90	91-100

SOLUTION

Suppose, random variable X denotes marks obtained by students in STA2020.

(a)

Required probability is given by

[Using R-code 'pnorm(-2)']

Hence, 2.28% students failed.

(b)

Required probability is given by

[Using R-code '1-pnorm(1.027027)']

Hence, 15.22% students obtained A+ grade.

(c)

Required probability is given by

[Using R-code ' pnorm(0.4324324)-pnorm(-0.05405405)']

Hence, 18.88% students obtained B+ grade.