What are the 4 conditions for Binomial distributions?

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Presentation transcript:

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 a 3 b) Find the probability that it takes less than 3 rolls to observe a 3