Question

3. a) Find the probability that at most 2 out of 50 given people will have invalid driver’s licenses if normally 5% of the people do. b) Use the Poisson approximation to calculate the above probability. c) Use the normal approximation to calculate the above probability.

Answer #1

Suppose 1% of people don’t have immunity against a new virus.
Let P be the probability that there are 2, 3 or 4 people without
immunity in a random sample of 100 people.
a) Use binomial distribution to find P.
b)Use normal approximation to the binomial distribution
to find P .
c) Use Poisson distribution to find P .

Suppose 1% of people doesn’t have immunity against a new virus.
Let P be the probability that there are 2, 3 or 4 people
without immunity in a random sample of 100 people.
Use binomial distribution to find P .
Use normal approximation to the binomial distribution to find
P .
Use Poisson distribution to find P .

A study on aggressive driving found that 50 % of drivers say
that they have yelled at another driver. A random sample of 180
drivers in Halifax is selected and are asked whether they have
yelled at other drivers.
a. What is the probability that at least 85 drivers will say
”yes”, they have yelled at another driver? [Hint: use normal
approximation]
b. What is the probability that at most 86 drivers will say
”yes”, they have yelled at another...

Find the probability of more than 30 heads in 50 flips of a fair
coin by using the normal approximation to the binomial
distribution.
a) Check the possibility to meet the requirements to use normal
approximation (show your calculation)
b) Find the normal parameters of the mean(Mu) and standard
deviation from the binomial distribution.
c) Apply normal approximation by using P(X>30.5) with
continuity correction and find the probability from the table of
standard normal distribution.

Suppose that on average 2 people in a major city die each year
from alien attack. Suppose that each attack is random and
independent.
(a) If X is the number of deaths from alien attack within the
next year from a randomly selected major city, what type of random
variable is X?
(b) Use the Poisson approximation to approximate the probability
that the next major city you visit will have at least 3 deaths due
to alien attack?
(c) Why...

Suppose the probability that a person has type O- blood is 0.05.
Consider a group of 200 people.
a. What is the probability that exactly 3 people of the people
in the group have type O- blood? (3 points)
b. Show that this binomial distribution satisfies both
conditions needed to use the normal approxi- mation to the
binomial. (2 points)
c. Using the normal approximation to the binomial, find the
probability that at least 13 people in the group have...

Blood type AB is found in only 3% of the population.† If 300
people are chosen at random, find the probability of the following.
(Use the normal approximation. Round your answers to four decimal
places.)
(a) 5 or more will have this blood type
(b) between 5 and 10 will have this blood type

Consider the probability that greater than 88 out of 152 people
have not been in a car accident. Assume the probability that a
given person has not been in a car accident is 66 % . Approximate
the probability using the normal distribution. Round your answer to
four decimal places.

45% of people have type O blood . If 400 volunteers show
up to donate blo, use the Normal approximation to the binomial to
find the probability that more than 175 but at most 182 have type O
blood.

Given that 1% of the population are left handed, if a random
sample of 1000 people is selected where x denotes the number of
left handed people,
a) The random variable X is (choose one)
i) Binomial
ii) hypergeometric
iii) Poisson
iv) Normal
v) Exponential
vi) Uniform
b) Give the expectation value and variance of X.
c) Find the probabilities P(X=6) and P(X≥6).
d) Which distribution from those listed in part (a) can be
used as an approximation to the...

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