statistics cheet sheet test 2
- The time for a professor to grade an exam is normally distributed with a mean of 12.6 minutes and a standard deviation of 2.5 minutes. What is the probability that a randomly selected exam will require more than 16 minutes to grade?
a.0.7734 normalcdf(16,1E99,12.6,2.5)
z | 0.00 | 0.01 | 0.02 | 0.03 | 0.04 | 0.05 | 0.06 | 0.07 | 0.08 | 0.09 |
1.2 | 0.8849 | 0.8869 | 0.8888 | 0.8907 | 0.8925 | 0.8944 | 0.8962 | 0.8980 | 0.8997 | 0.9015 |
1.3 | 0.9032 | 0.9049 | 0.9066 | 0.9082 | 0.9099 | 0.9115 | 0.9131 | 0.9147 | 0.9162 | 0.9177 |
1.4 | 0.9192 | 0.9207 | 0.9222 | 0.9236 | 0.9251 | 0.9265 | 0.9279 | 0.9292 | 0.9306 | 0.9319 |
- The time that customers wait to be served at the delicatessen for a grocery store follows the uniform distribution between 0 and 7 minutes. What is the probability that a randomly selected customer will wait more than 3 minutes at the deli? (Round the probability to four decimal places.)
- 0.5714 d.0.1429
- 0.2857 e.None of the above c.0.8571
Probability is found by the area of the red region:
- Which of the following is not a condition of a discrete probability distribution?
- Each outcome in the distribution needs to be mutually exclusive with other outcomes in the distribution.
- The sum of the probabilities for all the outcomes in the distribution needs to add up to 1.
- The probability of each outcome, P(x), must be between 0 and 1 (inclusive).
- The probability of a success must exceed the probability of a failure.
- None of the above
- The useful life for a certain automobile battery is normally distributed with a mean of 5 years. If 27% of these batteries have a useful life from 4.1 to 5.0 years, what percentage of batteries would last at least 5.9 years?
- 23%
- 27%
- 46%
- 54%
- None of the above
We are told the blue region has an area of 0.27. Since the normal is symmetric and both
4.1 and 5.9 are 0.9 units from the mean, then the red region must also have an area of 0.27. The red and green regions make up the entire right half of the normal and, therefore, must have a total area of 0.5.
Which leaves 0.5 – 0.27 = 0.23 as the area of the green region.
- Which of the following statements is true regarding z-scores for the normal probability distribution?
- z-scores are equal to 1.0 for values of x that are equal to the distribution mean.
- z-scores are positive for values of x that are larger than the distribution mean.
- z-scores are negative for values of x that are larger than the distribution mean.
- z-scores are zero for values of x that are larger than the distribution mean.
- None of the above
- Dempsey’s Garage repairs domestic and import cars. The following table shows the number of cars that have been serviced by age and type during the last month.
Age | Domestic | Import | Total |
0 to under 5 years old | 12 | 6 | 18 |
5 to under 10 years old | 24 | 9 | 33 |
10 to under 15 years old | 8 | 16 | 24 |
Total | 44 | 31 | 75 |
The probability (to three decimal places) that a randomly selected car from this group was from 5 to under 10 years old, given it was an import is ________.
- 0.273
- 0.290
- 0.325
- 0.359
- None of the above
- The following probability distribution shows the number of pieces of junk mail that arrives in John’s mailbox each day.
Number of Pieces of Junk | Probability |