Download STAT303 Exam #2 Fall 2000: Multiple Choice Questions on Probability and Statistics and more Exams Data Analysis & Statistical Methods in PDF only on Docsity!
STAT303: Secs 508-
Fall 2000
Exam
Form A
Julie Hagen Carroll
October 25, 2000
- Don’t even open this until you are told to do so.
- There are 20 multiple-choice questions on this exam, each worth 5 points. There is partial credit. Please mark your answers clearly on the exam. Multiple marks will be counted wrong.
- You will have 60 minutes to finish this exam.
- If you are caught cheating or helping someone to cheat on this exam, you both will receive a grade of zero on the exam. You must work alone.
- This exam is worth 100 points, and will constitute 20% of your final grade.
- Good luck!
- Which of the following is true about random sampling?
A. We use it to avoid biased estimates. B. The sample will cover all possible values. C. Each value of the population will be just as likely in the sample. D. All of the above are true. E. Exactly two of the above are true.
- For p 50 ∼ N (0. 5 , 0. 0712 ), what is P (p 50 < 0 .6)?
A. 1. B. 0. C. 0. D. 0. E. 0.
- For the distribution above, what is P (0. 5 < X < 1 .5)?
A. 0. B. 0. C. 0. D. 0. E. 0.
- Find the 65th percentile of the Standard Normal, Z ∼ N (0, 12 ).
A. 0. B. 0. C. 0. D. 0. E. 0.
- Suppose that we can assume the event ’rain on Friday’ is independent from week to week. If the probability of this event is 20%, what is the probability that it rains this Friday if we know it rained the last two Fridays?
A. Since the events are independent, it’s the product of their probabilities, 0. 203. B. Since the events are independent, it’s still 0.20. C. Since it’s a conditional probability, it’s
203 / 0 .20. D. Since the events are independent, it’s the sum of the probabilites, 0.20+0.20+0.20 = 0 .60. E. Since we can’t predict the weather, we can- not determine the probability.
Let x ∼ N (7. 2 , 1. 42 ). If we take a random sam- ple of size 49 from this population, what is the probability that the sample mean, X¯ 49 , will be between 7.1 and 7.4, i.e., find P (7. 1 < X¯ 49 < 7 .4)?
A. 0. B. 0. C. 0. D. 0. E. We don’t know the distribution of X¯ 49 , so we can’t determine the probability.
- According to the Central Limit Theorem, if you take many samples of size n from a given popula- tion and compute the sample mean, X¯, for each sample, then the resulting distribution of X¯ will
A. look like the distribution of the parent (original) population, provided n is large enough. B. look like a normal distribution, provided n is large enough. C. have the same variance as the parent pop- ulation no matter what the value of n is. D. have the same mean as the parent popula- tion no matter what the value of n is. E. have the same variance as the parent pop- ulation, provided n is large enough.
- What is x∗^ such that P (X < x∗) = 0.94 if X ∼ N (2, 52 )?
A. 1. B. 9. C. 3. D. 8. E. 0.
- Suppose that there are two different models of cars for rent. The gas mileage of both model A and B is approximately normal. The mean and standard deviation of A are 24 and 4 mpg. For B, they are 23 and 1 mpg, respectively. If your minimum acceptable gas mileage is 20 mpg, which model should you rent?
A. Model A since it has a better average mpg. B. Model B since it has a smaller standard de- viation for it’s mpg. C. Either model will be ok since both have av- erages above 20 mpg. D. Model B since it is unlikely it could get mpg below 20. E. Either model is acceptable since both are most likely over 20 mpg.
- If X ∼ N (3, 52 ) and Y = 7 − 5 X, what is the distribution of Y? Hint: remember this is just a shift and a scale on X!
A. N (− 8 , 11. 22 ) B. N (− 8 , − 52 ) C. N (− 8 , 252 ) D. N (8, 52 ) E. N (− 8 , 52 )
- Which of the following statements is true?
A. If P (A|B) = P (A), then A and B are mu- tually exclusive events. B. Two outcomes are independent if they can- not happen simultaneously. C. If two events are not independent, they have to be mutually exclusive. D. If two events, A and B, are mutually exclu- sive, then P (A or B) = P (A) + P (B), the union is just the sum. E. None of the above is true.
- What is z∗^ such that P (−z∗^ < Z < z∗) = 0. 75 and Z ∼ N (0, 12 )
A. 0. B. 1. C. 0. D. 0. E. 1.
- Which of the following are true?
A. Statistics vary from sample to sample, but parameters are always fixed numbers. B. All parameters have sampling distributions. C. A parameter is a function of sample out- comes.
D. All of the above are true. E. None of the above are true.
1A,2B,3C,4C,5B,6C,7B,8B,9C,10D,11E 12C,13E,14E,15C,16D,17C,18D,19B,20A
