PROBABILITY DISTRIBUTION OF DISCRETE VARIABLES
Binomial Distribution
Exercises
4.3.1 Based on their analysis of data collected by the National Center for Health Statistics , Researcher report that 25.7 percent of U.S. adults are overweight. If we select a simple random sample of 20 U.S. adults, find the probability that the number of overweight people in the sample will be (round the percentage to 26 for computation purposes):
(a) Exactly three
(b) Three or more
(c) Fewer than three
(d) Between three and seven, inclusive
ANSWER
(a) 0.1199
(b) 0.9237
(c) 0.0763
(d) 0.8012
4.3.7: The probability that a person suffering from migraine headache will obtain relief with a particular drug is 0.9. Three randomly selected suffers from migraine headache are given the drug. Find the probability that the number obtaining relief will be:
(a) Exactly zero
(b) Exactly one
(c) More than one
(d) Two or fewer
(e) two or three
(f) Exactly three
ANSWER
(a) 0.001
(b) 0.027
(c) 0.972
(d) 0271
(e) 0.972
(f) 0.729
Poisson Distribution
Exercise
4.4.1: Suppose it is known that in a certain area of a large city the average number of rats per quarter block is five. Assuming that the number of rats follows a Poisson distribution, find the probability that in a randomly selected quarter block:
(a) There are exactly five rats.
(b) There are more than five rats.
(c) There are fewer than five rats.
(d) There are between five and seven rats, inclusive.
ANSWER
(a) 0.176
(b) 0.384
(c) 0.440
(d) 0.427
CONTINUOUS PROBABILITY DISTRIBUTIONS
THE NORMAL DISTRIBUTION
EXCERCISES
4.6.1: The area under the curve between z=0 and z=1.43.
ANSWER
0.4236
4.6.3: P(Z>=0.55).
ANSWER
0.2912
4.6.4: P(Z>=-0.55).
ANSWER
0.7912
4.6.5: P(Z<-2.33).
ANSWER
0.0099
4.7.1: suppose the ages at time of onset of a certain disease are approximately normally distributed with a mean of 11.5 years and a standard deviation of 3 years. A child has just come down with the disease. Find the probability that the child is:
(a) Between the ages of 8.5 and 14.5 years
(b) Over 10 years of age
(c) Under 12
ANSWER
(a) 0.6826
(b) 0.6915
(c) 0.5675