The test result is not perfect to identify a drug user or a non-drug user.
The test result is not useful since the shaded areas in both D and N
populations are equally sized.
The test result is useful since the percentage of the shaded area is very
high in D population and very low in N population.
The positive test result is helpful in identifying a person who is a drug
user.
The negative test result is helpful in identifying a person who is a
non-drug user.
The download time of a 90 minutes movie is a normal distribution with
mean of 2 hours and standard deviation of 20 minutes. Given that a
download has lasted for 2 hours. What is the probability that the download
will finish in 30 minutes. (5%)
Phone calls arrive with Poisson distribution at the rate of 48 per hour.
What is the probability of receiving three or more calls in five minutes?(5%)
Let X be the random variable of service time. A service level, defined as the
probability of non-waiting service, of 90% is set by the company policy.
Please find the 90th percentile, P(X ≤ X 0.90 ) = 0.90 , of the following service
time distribution.
(1) Normal service time with mean equals 8 minutes and standard
deviation equals 2 minute. (5%)
(2) Exponential service time with mean equal 8 minutes. (5%)
Construct the sampling distribution of the number of computers sold in
two days, i.e., the random variable of X1 + X2 and its corresponding
probability. (10%)
Below is the description of how a recent poll was conducted by the WYZ
company on political issues. The latest WYZ poll is based on telephone
interviews conducted from Jan. 10 through June 17 with 1,050 adults
throughout the United States. The sample of telephone exchanges called
was randomly selected by a computer from a complete list of more than
42,000 active residential exchanges across the country. Within each
exchange, random digits were added to form a complete telephone number.
Within each household, one adult was designated by a random procedure
to be the respondent for the survey. In theory, in 19 cases out of 20, the
results based on such samples will differ by no more than three percentage
points in either direction from what would have been obtained by seeking
out all American adults. However, in addition to sampling error, the
practical difficulties of conducting any survey of public opinion may
introduce other sources of error into the poll.
(1) What kind of survey subjects is included in the WYZ sampling frame?(5%)
(2) Why was the benefit of WYZ’s sampling scheme compared with the from
current telephone books? (5%)
(3) What was the confidence level in this survey? How much was the
margin of error? How was the margin of error obtained? (5%)
(4) What other possible error would involve by telephone interviews in practice? (5%)
In science, size plays an essential role is describing natural competition.
Over time, scientists have conjectured that the size of human’s brain is
related to his IQ (a measure of intelligence). Suppose that data about the
size of brains (head circumferences) and the associated IQs are sampled
and collected as shown in the following:
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