2.2Probability Distributions
Problems 1-5 are worth 6 points each; 6 and 7 are worth 10 points each
1. A ____ simply lists all the possible outcomes of an experiment and tallies the number of times each outcome occurs. By contrast, a ___ graphs the probability of all the possible outcomes of the variable instead of their frequency. | |
2. In a normal distribution, the ____, _____, and the ___ are all the same. They are denoted by the Greek letter ___. | |
3. The test statistic calculated from the normal distribution is called the ____. | |
4. Generally, to use the Central Limit Theorem, a sample size should be greater than ____. | |
5. If a distribution describes events that usually occur a certain number of times within a given time period, the distribution is not ___ because if it were, the tail would have to extend to less than ___ in order for the tails to extend equal distances from the ____ (be symmetrical). Instead, when graphed, the distribution is “cut off” on the left side but has a tail to the right. This distribution is called a _____ distribution. In this distribution, the _____ and the ____ are equal and are denoted by the Greek letter __. | |
- A medical student took a standardized achievement test. In a test population of medical students, the scores were normally distributed. On this test, the mean score is 500 and the standard deviation is 100. The student’s reported score was 713.
- Calculate the student’s Z-score.
- In words, what is the interpretation of the Z-score?
- If this student is in a class of 200 and their scores are normally distributed, how many students in the class would be expected to equal or surpass this student’s score? Round to the nearest whole student. (You may use a textbook or on-line tool of your choice.)
- In a certain military detachment deployed overseas, the soldiers received an average of two letters per week at mail call. Using the on-line calculator determine the probability that a soldier in the detachment would receive:
- Exactly three letters in a week.
- Three or more letters in a week.
- No letters at all in a week.