Question

4. A top brand of a popular pickup truck's life is normally distributed with its mean, 12 years and standard deviation, 4 years. Suppose that the top executives of the automaker decided that only 1.2% of new trucks sold could be replaced with a new truck or fully refunded within the warranty period. What should be a desirable warranty period? 5. The grade distribution of a basic English course in a high school (total 3500 students) is normally distributed with its mean, 3.2 and standard deviation, 0.61. 1) If a student is randomly selected, find the probability that the student's score is higher than 2.0? 2) If you collect a sample of 30 students, what is the probability that the sample mean is less than 3.5?

Answer 1

$\mu$ = 12 years

$\sigma$ = 4 years

1.2% = 0.012

(4)

when area =0.012

value of Z = - 2.257

let desirable warranty = x years

so we have

T 11 Z=

$-2.257=\frac{x-12 }{4 } \Rightarrow x= 2.972$

x= 2.972 years Answer

(5)

When x=2

Z 2 - 3.2 0.61 = -1.9672

P( x > 2) = 1- area from left to (z=-1.9672)

= 1- 0.02458

= 0.97542 Answer

(6)

When n= 30

= 3.5

T

$Z=\frac{\bar{x}-\mu }{\sigma/\sqrt{n} }$

$Z=\frac{\bar{x}-\mu }{\sigma/\sqrt{n} }=\frac{3.5-3.2}{4/\sqrt{30}} =0.41079$

P( <  3.5) = area from left to( Z= 0.41079)

T

= 0.6594 Answer