Question

1. QD Corporation makes paints known for their quality and quick drying features. QD has developed a new wall paint code named Mickey that it is testing in a controlled environment. The firm is testing for drying time of the paint. Drying time is affected by factors like humidity, air pollution, ventilation and temperature. The test results show that the drying time of Mickey is normally distributed with a mean of 10 hours and a standard deviation of 1.8 hours.

Compute the following:

1. What is the probability that the drying time is less than 7 hours?
2. What is the probability that the drying time is between 6 hours and 12 hours?
3. What should the label on the paint can say if the firm wants to be 95% sure that the drying time will be the claimed time or less?
4. A customer returns a can saying that the drying time was 15 hours. What is the z score corresponding to that observed value?

Answer 1

(a)

= 10

= 1.18

To find P(X<7):

Z = (7 - 10)/1.8

= - 1.67

Table of Area Under Standard Normal Curve gives area = 0.4525

So,

P(X<7) = 0.5 - 0.4525 = 0.0475

So,

Answer is:

0.0475

(b)

= 10

= 1.18

To find P(6<X<12):

Case 1 For X from 6 to mid value:

Z = (6 - 10)/1.8

= - 2.22

Table of Area Under Standard Normal Curve gives area = 0.4868

Case 2 For X from mid value to 12:

Z = (12 - 10)/1.8

= 1.11

Table of Area Under Standard Normal Curve gives area = 0.3665

So,

P(6<X<12) = 0.4868 + 0.3665 = 0.8533

So,

Answer is:

0.8533

(c)

85% corresponds to area = 0.85 - 0.50 = 0.35 from mid value to Z on RHS.

Table gives Z = 1.04

So,

Z = 1.04 = (X - 10)/1.8

So,

X = 10 + (1.04 X 1.8)

= 11.872

So,

Answer is:

11.872

(d)

X = 15

So,

Z = (15 - 10)/1.8

= 2.7778

So,

Answer is:

2.7778