Statistics
Carlito Van
DSC210Exam_3SP2018_1_11.docx
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(100 points)
1. Match each of the descriptions on the left with the correct lettered terms on the right. Each letter is used once, or not at all. (2 points each)
____ A continuous probability distribution A. Central Limit Theorem.
for which the probability that the random B. Z-number.
variable takes a value in an interval is the C. Normal.
same for equal-length intervals. D. Census.
like a normal random variable under F. Sampling Distribution.
certain conditions. G. Uniform.
____ A number that describes some trait, H. Standard Error.
or feature, of a population. I. Statistic.
____ A data set made up of observations J. Sample.
on every element in the population. K. Parameter.
____ A probability distribution whose
primary defining characteristic is
a symmetric, bell-shaped curve.
____ A probability distribution for a
sample statistic.
____ A normal random variable minus
its mean, divided by its standard
deviation.
2. The mean GPA for the all of the current undergrads at The Ohio State University is 2.05, with a standard deviation of 1.75. Assume that the GPAs are normally distributed. What is the value of the GPA that is the Upper Quartile in this distribution? (10 points)
3. Each sample statistic on the left is used as a point estimator of one of the population parameters on the right. Match them up correctly. Each letter is used once, or not at all. (2 points each)
4. Last year, the mean education-related debt for graduating college students was $31,400. Assume that the actual amount of debt for graduating college students follows a normal distribution with a standard deviation of $7421. If a simple random sample of 10 recently graduated college students is taken: (5 points each)
a. What is the probability that the sample mean education-related debt will exceed $35,000?
b. What is the probability that the sample mean education-related debt will fall between $25,000 and $33,500?
5. Given that z is the standard normal random variable, find z for each situation:
(5 points each)
a. The area to the right of z is 0.8264.
7. If the population proportion is 0.45, and a simple random sample of size 85 will be taken:
b. What is the probability that the sample proportion will take a value between 0.37 and 0.55? (5 points)
8. Given that z is the standard normal random variable, sketch the appropriate figure that accompanies each probability (complete with the appropriate shading to represent the probability), and compute the following probabilities: (5 points each)
a.
b.
9. The talk-time for a cellphone battery is the amount of time that a cellphone may be in continuous use before needing to recharge the battery. Samsung has just released a new cellphone with what is claimed to be a “revolutionary” new kind of battery that will have a significantly longer talk-time than other brands before needing to be recharged. Tests have shown that the talk-time for one of these new batteries, before needing to be recharged, follows a continuous Uniform distribution between 20 and 28 hours. Let T = the actual amount of talk-time for one of these batteries.
a. Sketch the graph of the pdf of T. (5 pts)
b. Calculate the probability that the talk-time for one of these batteries will exceed 27 hours. (5 points)
c. What is the probability that the talk-time for one of these batteries will be exactly 25 hours? (5 points)
d. What is expected number of hours of talk-time for one of these batteries? (5 pts)
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