Worksheet 5 – Elementary Statistical Methods
Names: ___________________________________________________
- Determine whether the distribution represents a probability distribution. If it does not, state why.
| X | 15 | 16 | 20 | 25 |
| P(X) | 0.6 | 0.5 | 0.7 | −0.8 |
| X | −5 | −3 | 0 | 2 | 4 |
| P(X) | 0.1 | 0.3 | 0.1 | 0.3 | 0.1 |
| X | 20 | 30 | 40 | 50 |
| P(X) | 0.05 | 0.35 | 0.4 | 0.2 |
- Mathematics Tutoring Center.At a drop-in mathematics tutoring center, each teacher sees 5 to 9 students per hour. The probability that a tutor sees 5 students in an hour is 0.107; 6 students, 0.125; 7 students, 0.298; and 9 students, 0.342. Find the probability that a tutor sees 8 students in an hour and construct the probability distribution.
- Traffic Accidents.The county highway department recorded the following probabilities for the number of accidents per day on a certain freeway for one month. The number of accidents per day and their corresponding probabilities are shown. Find the mean, variance, and standard deviation.
| Number of accidents X | 0 | 1 | 2 | 3 | 4 |
| Probability P(X ) | 0.31 | 0.18 | 0.17 | 0.15 | 0.19 |
- Benford’s LawThe leading digits in actual data, such as stock prices, population numbers, death rates, and lengths of rivers, do not occur randomly as one might suppose, but instead follow a distribution according to Benford’s law. Below is the probability distribution for the leading digits in real-life lists of data. Calculate the mean, variance, and standard deviation. for the distribution.
| X | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| P(X) | 0.201 | 0.070 | 0.125 | 0.187 | 0.179 | 0.077 | 0.048 | 0.057 | 0.056 |
- Dice Game.A person pays $3 to play a certain game by rolling a single die once. If a 1, 2, or 3 comes up, the person wins nothing. If, however, the player rolls a 4, 5, or 6, she or he wins the difference between the number rolled and $3. Find the expectation for this game. Is the game fair?
- Life Insurance.A 55-year-old man purchases a $250,000 term life insurance policy for an annual payment of $760. Based on a period life table for the U.S. government, the probability that he will survive the year is 0.9981321. Find the expected value of the policy for the insurance company.
- Compute the probability of Xsuccesses, using Table B from the textbook.
- n= 14, p = 0.80, X = 10
- n= 15, p = 0.05, X = 0
- n= 20, p = 0.50, X = 12
- n= 16, p = 0.20, X = 6
- Belief in UFOs.A survey found that 10% of Americans believe that they have seen a UFO. For a sample of 10 people, find each probability using the binomal distribution formula:
- That at least 3 people believe that they have seen a UFO
- That at most 3 people believe that they have seen a UFO
- That exactly 5 people believe that they have seen a UFO
- Watching Fireworks.A survey found that 37% of Americans watched fireworks on television on July 4, 2020. Find the mean, variance, and standard deviation of the number of individuals who watch fireworks on television on that day if a random sample of 2200 Americans is selected.
- Alternate Sources of Fuel.Seventy-seven percent of Americans favor spending government money to develop alternative sources of fuel for automobiles. For a random sample of 215 Americans, find the mean, variance, and standard deviation for the number who favor government spending for alternative fuels.