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# Statistics: final exam

The final exam for Statistics: course.

1. The blood urea nitrogen count of 20 randomly selected patients is given: 17, 18, 13, 14, 12, 17, 11, 20, 13, 18, 19, 17, 14, 16, 17, 12, 16, 15, 19, 22. Construct a histogram, a frequency polygon, and an ogive (the cumulative distribution function) for the data.

2. The number of highway miles per gallon of the worst 10 vehicles is given: 12, 15, 13, 14, 15, 16, 17, 16, 17, 18. Find the following: mean, median, mode, midrange, range, variance, standard deviation.

3. The distribution of the number of errors that 10 students made on a typing test is shown. (a) Find the mean. (b) Illustrate the data with a pie-chart.

Errors |
Frequency |

0-2 |
1 |

3-5 |
3 |

6-8 |
4 |

9-11 |
1 |

12-14 |
1 |

4. The number of square feet (in millions) of eight of the largest malls in SW Pennsylvania is given: 1.00, .90, 1.30, .80, 1.40, .77, .70, 1.20. (a) Find the percentile for each value. (b) What value corresponds to the 40th percentile? (c) Construct the box-plot and comment on the nature of the distribution.

5. When two dice are rolled, find the probability of the following: (a) a sum of 5 or 6. (b) a sum less than 13, (c) a sum of 1, (d) a double.

6. A manufacturing company has three factories: X, Y, and Z. The daily output of each is shown. If one item is selected at random, find these probabilities: (a) it was manufactured at factory X and it is a stereo, (b) it was manufactured at factory Y or factory Z, (c) it was a TV or it was manufactured at factory Z.

Product |
Factory X |
Factory Y |
Factory Z |

TV’s |
18 |
32 |
15 |

Stereos |
6 |
20 |
13 |

7. How many different ways can 8 computer operators be seated in a row?

8. A newspaper advertises 5 different movies, 3 plays, and 2 basketball games for the weekend. If the couple selects 3 activities, find the probability that they attend 2 plays and 1 movie.

9. A box contains 5 pennies, 3 dimes, 1 quarter, and a half-dollar. Construct a probability distribution and draw a graph for the data.

10. During a paint sale, the number of cans of paint purchased was distributed as shown. Find the expected value of the number of cans and the standard deviation.

Number of cans |
1 |
2 |
3 |
4 |
5 |

Probability P(X) |
.42 |
.27 |
.15 |
.10 |
.06 |

Extra credit. An ogive is given below. Plot the corresponding histogram.