Bus Statistics Exam
| The director of admissions at Kinzua University in Nova Scotia estimated the distribution of student admissions for the fall semester on the basis of past experience. |
| Admissions | Probability |
| 1,050 | 0.3 |
| 1,280 | 0.1 |
| 1,560 | 0.6 |
| 1. | What is the expected number of admissions for the fall semester? 5309 |
| Expected number of admissions: 1379 |
| 2. | Compute the variance and the standard deviation of the number of admissions. (Round your standard deviation to 2 decimal places.) |
| Variance :53109 | |
| Standard deviation: 230.45 |
2.
| It is asserted that 70% of the cars approaching an individual toll booth in New Jersey are equipped with an E-ZPass transponder. Find the probability that in a sample of five cars: |
| a. | All five will have the transponder. (Round your answer to 4 decimal places.) |
| Probability: 0.1681 |
| b. | At least three will have the transponder. (Round your answer to 4 decimal places.) |
| Probability: 0.8369 |
| c. | None will have a transponder. (Round your answer to 6 decimal places.) 0.002430 |
| Probability: 0.00243 |
3.
| The Internal Revenue Service is studying the category of charitable contributions. A sample of 24 returns is selected from young couples between the ages of 20 and 35 who had an adjusted gross income of more than $100,000. Of these 24 returns, 8 had charitable contributions of more than $1,000. Suppose 7 of these returns are selected for a comprehensive audit. | |
| a | You should use the hypergeometric distribution is appropriate. Because |
| hypergeometric distribution is appropriate because the selection is without replacements | |
| b. | What is the probability exactly one of the seven audited had a charitable deduction of more than $1,000? (Round your answer to 4 decimal places.) | |||
| Probability | 0.1851 | |||
| c. | What is the probability at least one of the audited returns had a charitable contribution of more than $1,000? (Round your answer to 4 decimal places.) |
| Probability: 0.9669 |
| Recent crime reports indicate that 4.8 motor vehicle thefts occur each minute in the United States. Assume that the distribution of thefts per minute can be approximated by the Poisson probability distribution. |
| a. | Calculate the probability exactly three thefts occur in a minute. (Round your answer to 3 decimal places.) |
| Probability: 0.152 |
| b. | What is the probability there are no thefts in a minute? (Round your answer to 3 decimal places.) |
| Probability: 0.008 |
| c. | What is the probability there is two or less thefts in a minute? (Round your answer to 3 decimal places.) |
| Probability: 0.143 |
| The mean of a normal probability distribution is 320; the standard deviation is 18. |
| a. | About 68% of the observations lie between what two values? |
| Value 1: 302 | |
| Value 2: 388 | |
| b. | About 95% of the observations lie between what two values? |
| Value 1: 284 | |
| Value 2: 356 | |
| c. | Practically all of the observations lie between what two values? |
| Value 1: 266 | |||||||||||||||||||||||||||||||||||||||||||||
| Value 2: 375 | |||||||||||||||||||||||||||||||||||||||||||||
6.
7.
8.
|
|||||||||||||||||||||||||||||||||||||||||||||
