Question

7. The mean weight of students from a certain university is 70 kg with a standard deviation

of 17 kg. i.

ii. iii.

Assume that the weights of students in the university are normally distributed.

What is the probability that the weight of a randomly chosen student is greater than 100 kg?

What is the probability that the weight of a randomly chosen student is between 60 kg and 80 kg?

If you were to take a sample of 16 students, what is the probability that the mean of this sample is more than 73 kg?

Answer 1

(i)

= 70

= 17

To find P(X>100):

Z = (100 - 70)/17 = 1.76

Table of Area Under Standard Normal Curve gives area = 0.4608

So,

P(X>100) = 0.5 - 0.4608 = 0.0392

So,

Answer is:

0.0392

(ii)

= 70

= 17

To find P(60<X<80):

Case 1: For X from 60 to mid value:

Z = (60 - 70)/17 = - 0.59

Table of Area Under Standard Normal Curve gives area = 0.2224

Case 2: For X from mid value to 80:

Z = (80 - 70)/17 = 0.59

Table of Area Under Standard Normal Curve gives area = 0.2224

So,

P(60<X<80) = 2 X 0.2224 = 0.4448

So,

Answer is:

0.4448

(iii)

n = 16

SE = /

= 17/ = 4.25

To find P( > 73):
Z = (73 - 70)/4.25 = 0.71

Table gives area = 0.2611

So,

P( > 73) = 0.5 - 0.2611 = 0.2389

So,

Answer is:

0.2389