Tutorial 3

of this tutorial:

Understand the conditions under which binomial distributions occur Recognise and define binomial random variables

Calculate binomial probabilities

Calculate probabilities and values for normally distributed random variables

If two carriers of the gene for albinism have children, each child independently has a probability of 14 of being albino.

(a) Consider six children born to such couples, and let X be a random variable representing the number of albinos among these children. Explain why X will follow a binomial distribution.

(b) Identifytheprobabilitydistributionofthisvariableintermsofitsnameandparameters.

(c) What is the probability that, out of six children born to such couples,

(i) none will be albino (ii) at most 3 will be albino,

(iii) atleast2willbealbino, (Iv) atleast1willnotbealbino?

(d) Considerthedistributionofthenumberofalbinochildrenborntocoupleswhobothhave the gene for albinism. That is, we are now interested in the number of albino children per couple, among couples who both carry the gene. Either state what the distribution is, or explain why you cannot state what it is.

A study of trees with diameter 12 inches in the Ozark Highlands area of Missouri found that there is a nine to one chance that such a tree survives the next five years.

Assuming that survival of such trees is independent -

(a) What is the probability distribution for the number of trees which survive the next five years, out of a random sample of 25 trees.

(b) Statetheprobabilitydistributionforthenumberoftrees,outofarandomsampleof18, which don't survive the next five years.

(c) For a random sample of 20 such trees calculate -

(i) the mean, and

(ii) the standard deviation

of the number of trees that will survive the next five years.