# Mathematics

QNT 351 – No. 3

(show your work – 15 pts each)

Name:

QNT 351 2 No. 3

1-If 90 percent of automobiles in Orange County have both headlights working, what is the probability that in a sample of 8 automobiles, at least 7 will have both headlights working?

A) 0.8131

B) 0.3826

C) 0.0351

D) 0.875

2-The following table lists the probability for cash prizes in a lottery conducted at Lawson’s Department Store.

 Prize (\$) Probability 0 0.45 10 0.30 100 0.20 500 0.05

a) What is the probability to win \$100?

b) What is probability to win more than 10?

c) Compute the expected cash prize?

3- The normal curve can be fully described by the

A) standard deviation.

B) mean.

C) standard deviation and the mean.

D) None of the above, not enough information.

Use the following to answer questions 4 thru 6

The MPG (miles per gallon) for a certain compact car is normally distributed with a mean of 31 and a standard deviation of 0.8.

4- What is the probability that the MPG for a randomly selected compact car would be less than 31?

5- What is the probability that the MPG for a randomly selected compact car would be more than 32?

6- What is the probability that the MPG for a randomly selected compact car would be between 31 to 33?

Use the following to answer questions 7 and 8

The time required for a citizen to complete the 2000 U.S. Census “long” form is normally distributed with a mean of 40 minutes and a standard deviation of 10 minutes.

7- What is the cut-off time between the slowest 10% and the fastest 90% of the population to fill out the form?

8- What are the time limits for the middle 90% of the population to fill out the form?

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