What are the 4 conditions for Binomial
distributions?
Are the following binomial distributions or not?
a) You want to know what percent of married
people believe that mothers of young children
should not be employed outside the home. You
plan to interview 50 people, and for the sake of
convenience you decide to interview both the
husband and the wife in 25 married couples. The
random variable X is the number among 50
persons interviewed who think mothers should not
be employed.
20% of American households own 3 or more motor vehicles. You
choose 12 households at random.
a) What is the probability that none of the chosen households own 3
or more vehicles? What is the probability that at least one
household owns 3 or more vehicles?
b) What are the mean and standard deviation of the number of
households in your sample that own 3 or more vehicles.
Let X = number of boys in a family of 7 children. Assume that
sons and daughters are equally likely outcomes. Do you think the
distribution of X will be skewed left, symmetric, or skewed right?
The answer to this question depends on what fact?
After answering the above question, construct a probability
distribution table. (hint use binompdf)
In a survey conducted by North Carolina Institute inSocial
Science, they found that 46% of southerners believe
they have been healed by prayer. Suppose that 20
southerners selected at random and are asked if they
believe they have been healed by prayer. Find the
probability that the number who answer “yes” to this
question is:
a) Exactly 10
b) Between 10 and 15
c) Over 75% of 20
d) Less than 8
About 12% of American adults are black. The number X of blacks in
a random sample of 1500 adults should vary with the binomial
distribution (n=1500 p=.12)
a)What are the mean and standard deviation of X
b) Use the normal approximation to find the probability that the
sample will contain between 165 and 195 blacks.
Suppose that Roberto, a major league baseball player finished last
season with a .325 batting average. He wants to calculate the
probability that he will get his first hit of the new season in his
first at bat. You define a success as getting a hit and define the
random variable X= number of at bats until Roberto gets his first
hit.
a) What is the probability that Roberto will get a hit on his first at
bat?
b) What is the prob that it will take him at most 3 at bats to get his
first hit?
c) What is the prob. that it will take him more than 4 at bats to get his
first hit?
d) What is his expected number of at bats until he gets a hit. (mean)
Roll a die
a) Find the probability that it takes more than 10 rolls to observe
a3
b) Find the probability that it takes less than 3 rolls to observe a 3