Statistics Review Day 2 – Chapters 3 and 4

  1. In an advertisement, a retail store stated that its employees averaged 9 years of service. The dsitrbution is shown here.

Number of employees Years of service

82

26

310

Using the weighted mean, calculate the correct average.

  1. The average number of newspapers for sale in an airport newsstand is 12, and the standard deviation is 4. The average age of the pilots is 37 years, with a standard deivation of 6 years. Which data set is more variable?
  1. Find the weighted mean for a particular student’s scores on three exams if the first on was worth 75 points and the student received a score of 70%. The second was worth 50 points and the student received a score of 80%, and the third was worth 30 points and the student received a score of 95%.

5. The following data lists the number of children who attend an after-school program over an 11-day period. (sample)

2022293749566470 70 87 92

Find the:

  1. Meanb. Medianc. Moded. Midrange
  1. Rangef. Varianceg. Standard Deviation
  1. Use Chebyshev’s theorem to find the range in which at least 75% of the data values will fall.
  1. Find the percentile rank of 87.
  1. Which value corresponds to the 30th percentile?
  1. Make a (modified) boxplot and comment on its shape.

6. The number of home runs hit by the leaders in the National League during the 2001 MLB seasons had a mean of 37.9 and a standard deviation of 11. Find the minimum percentage of data values that will fall within the range of 15.9 and 59.9 home runs. Use Chebyshev’s Theorem.

7. Use the following data representing tornadoes per year in Oklahoma from 1995 until 2004, to construct a modified box plot.

79 / 47 / 55 / 83 / 145 / 44 / 61 / 18 / 78 / 62
  1. If one card is drawn from an ordinary deck of cards, what is the probability that the card will be a queen of diamonds, a black jack, or a club?

9. A recent poll found that 30% of those surveyed are worried about aggressive drivers on the road. If two people are selected at random, what is the probability that both will be worried about aggressive drivers on the road?

10. In a second grade class containing 12 girls and 10 boys, 2 students at random to give out the math papers. What is the probability that both are girls?

11. A group of 10 male and 8 female students is talking about going out for pizza. If 50% of the male students actually go and 25% of the female students actually go, find the probability that a random student who goes out for pizza is male.

12. In the Happy Hilltop Health Home, 20% of the residents play shuffleboard, 35% of the residents play poker, and 15% of the residents garden. If 5% of the residents play poker and garden, find the probability that a resident gardens, given that they also play poker.

13. There are 5 different mathematics courses, 4 different science courses, and 7 different history courses. If a student must take one of each, how many different ways can this be done?

14. Each of 10 students wishes to buy a particular textbook, but only 5 textbooks are available. How could one express the number of ways those textbooks could be distributed among the students?

15. A business has eight locations to choose from and wishes to rank only the top three locations. How many different ways can this be done?

16. It has been reported that 3% of all cars on the highway are traveling at speeds in excess of 70 mph. If the speeds of four random automobiles are measured via radar, what is the probability that at least one car is going over 70 mph?

17.a. Evaluate the following without a calculator: 8P4.

b. Evaluate the following without a calculator: 9C5.