Dean Chalmers and Julian Gilbey Solutions for Chapter: The Binomial and Geometric Distributions, Exercise 5: EXERCISE 7B

Give a reason why a binomial distribution would not be a suitable model for the distribution of $X$ in the following situation,

$X$ is the height of the tallest person selected when three people are randomly chosen from a group of $10$.

Give a reason why a binomial distribution would not be a suitable model for the distribution of $X$ in the following situation,

$X$ is the number of girls selected when two children are chosen at random from a group containing one girl and three boys.

Give a reason why a binomial distribution would not be a suitable model for the distribution of $X$ in the following situation,

$X$ is the number of motorbikes selected when four vehicles are randomly picked from a car park containing $134$ cars, $17$ buses and nine bicycles.

It is estimated that $1.3\%$ of the matches produced at a factory are damaged in some way. A household box contains $462$ matches. Calculate the probability that at least one from a sample of two household boxes contains exactly eight damaged matches.  [Write your answer correcting to three decimal places]

On average, $8\%$ of the candidates sitting an examination are awarded a merit. Groups of $50$ candidates are selected at random. How many candidates in each group are not expected to be awarded a merit $?$

On average, $8\%$ of the candidates sitting an examination are awarded a merit. Groups of $50$ candidates are selected at random. Calculate the variance of the number of merits in the groups of $50$.

On average, $8\%$ of the candidates sitting an examination are awarded a merit. Groups of $50$ candidates are selected at random. Find the probability that three, four or five candidates in a group of $50$ are awarded merits.  [Write your answer correcting to three decimal places]

On average, $8\%$ of the candidates sitting an examination are awarded a merit. Groups of $50$ candidates are selected at random. Find the probability that three, four or five candidates in both of two groups of $50$ are awarded merits.  [Write your answer correcting to three decimal places]