Question

We interviewed 1,000 QC students. On average they pay about $300 per semester to buy books and school materials, and they vary by $100.

1. Jason spent $400. How many students paid more than Jason?

2. Mary paid $200. How many paid less than her?

3. how many students paid an amount between Mary and Jason?

4. What is the price students are willing to pay, for the highest 10% ?

5. What is the price students are willing to pay, for the lowest 25% ?

Answer 1

(1)

= 300

= 100

To Find P(X>400):

Z = (400 - 300)/100 = 1

Table of Area Under Standard Normal Curve gives area = 0.3413

So,

P(X>400) = 0.5 - 0.3413 = 0.1587

So,

Number of students who paid more than Jason = 0.1587 X 1000 = 158.7 = 159 (Rounded to integer)

So,

Answer is:

159

(2)

= 300

= 100

To Find P(X<200):

Z = (200 - 300)/100 = - 1

Table of Area Under Standard Normal Curve gives area = 0.3413

So,

P(X<200) = 0.5 - 0.3413 = 0.1587

So,

Number of students who paid less than Mary = 0.1587 X 1000 = 158.7 = 159 (Rounded to integer)

So,

Answer is:

159

(3)

= 300

= 100

To Find P(200<X<400):

Case 1: For X from 200 to mid value:

Z = (200 - 300)/100 = - 1

Table of Area Under Standard Normal Curve gives aea = 0.3413

Case 2: For X from mid value to 400:

Z = (400 - 300)/100 = 1

Table of Area Under Standard Normal Curve gives aea = 0.3413

So,

P(200<X<400) = 2 X 0.3413 = 0.6826

So,

Number of students who paid between Mary and Jason = 0.6826 X 1000 = 682.6 = 683 (Rounded to integer)

So,

Answer is:

683

(4)

Highest 10% corresponds to area = 0.50 - 0.10 = 0.40

Table gives Z = 1.28

So,

Z = 1.28 = (X - 300)/100

So,

X = 300 + (1.28 X 100) = 428

So,

Answer is:

428

(5)

Lowest 25% corresponds to area = 0.50 - 0.25 = 0.25

Table gives Z = - 0.675

So,

Z = - 0.675 = (X - 300)/100

So,

X = 300 - (0.675 X 100) = 232.5 = 233 (Rounded to integer)

So,

Answer is:

233