# 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?