Description
(Problems 1-5)
#1. A city temperature is modeled as a normal random variable with mean and standard deviation both
equal to 10 degrees Celsius. What is the probability that the temperature at a randomly chosen time
will be less or equal to 15 degrees Celsius?
#2. A popular news magazine wants to write an article on how much Americans know about
geography. They devise a test that lists 100 cities in the US, all of them mentioned in the news
magazine in the last year. Each respondent must guess the state in which the city can be found.
Some examples were: (Los Angeles, Tuscon, Biloxi.) Each correct answer earns one point.
Assume the scores have normal distribution with mean 62 and standard deviation 12.
a) What is the probability of scores are between 50 and 74 points?
b) A score of 45 is considered a poor performance. What percentage of scores is below this
score?
#3. A population of widgets produce by a machine has weights with mean of 200mg and standard
deviation of 10mg. if a random sample of 36 widgets were taken,
a) what is the probability that the mean weight is at least 196mg?
b) What is the probability that the total weight is at most 3100mg?
#4. Suppose X is standard normal and
: 0
: 0
X
X
X
X
Y .
(a) Can transformation method be used to find the pdf of Y? If yes find pdf Y using
transformation method.
(b) Find pdf Y using cdf method.
#5. Suppose X is exponential with parameter
and
X
Y e .
(a) Can transformation method be used to find the pdf of Y? If yes find pdf Y using
transformation method.
(b) Find pdf Y using cdf method.
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Suggested Problems
Chapter-5: 19,20,21,23,25, Chapter-6: 21,23,25,26,27.
