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EQT 272 Probability and Statistics
Semester II
2015/2016
1. On the average, 12 people per hour approach a decorating consultant questions in a
fabric store. What is the probability that at least three people will approach the
consultant with questions during 10-minute period?
2. Suppose that 0.03% of plastic containers manufactured by a certain process have
small hotels that render them unfit for use. Let X represent the number of containers
in a random sample of 10000 have this defect. Find
i) P  X  3
ii) P  X  2
iii) P 1  X  4
iv) E  X  , V  X 
3. Overflow of flood results in the closure of a causeway. From past records, the road is
closed for this reason on 10 days during a 20-year period. At a village, the villagers
were concern about the closure of the causeway because the causeway provides the
only access for the villagers to go to another village nearby.
i) Determine the probability that the road is closed is between 2 and 6 days in
five years period.
ii) The villagers assumed that the probability of the closure of the road is more
than one day during a year is less than 0.10. Is the villagers assumption is
correct?
4. In San Francisco, 30% of workers take public transportation daily.
i) In a sample of 10 workers, what is the probability that exactly three workers
take public transportation daily?
ii) In a sample of 10 workers, what is the probability that at least three workers
take public transportation daily?
5. The unemployment rate is 5.8%. Suppose that 100 employable people are selected at
random.
i) What is the expected number who is unemployed?
ii) What are the variance and standard deviation of the number who is
unemployed?
iii) What is the probability that exactly six are unemployed?
iv) What is the probability that at least four are unemployed?
6. The average travel time to work for New York City Residents is 36.5 minutes.
i) What is the probability it will take a typical New Yorker between 20 and 40
minutes to travel to works?
ii) What is the probability it will take a typical New Yorker more than 40 minutes
to travel to works?
7. A particular production process used to manufacture ferrite magnets used to operate
reed switches in electronics meters is known to give 10% defective magnets on
average. A sample of 200 magnets is randomly selected.
i) What are the mean, variance, and standard deviation?
EQT 272 Probability and Statistics
Semester II
2015/2016
ii) What is the probability that the number of defective magnets is between 24
and 30?
8. The heights of boys at a particular age follow a normal distribution with mean
150.3cm and variance 25 cm. Find the probability that a boy picked at random from
this age group has height
i) Less than 153 cm
ii) More than 158 cm
iii) Between 150cm and 158 cm
iv) More than 10 cm difference from the mean height
9. 10% of the chocolate produced in a factory are mis-shapes. A random sample of 1000
chocolates taken. Find the probability that
i) Less than 80 are misshape
ii) From 90 to 115 are misshape
iii) 120 or more are misshape
10. The number of calls per hour received by an office switchboard follows a Poisson
distribution with parameter 30. Using the normal approximation to the Poisson
distribution, find the probability that in one hour,
i) There are more than 33 calls
ii) There are between 25 and 28 calls
iii) There are 34 calls.