Question

Approximately 6.85 left-handed people are killed each day by using an object or machinery designed for right-handed people. Let X be the number of left-handed people killed this way in one day.

a. What values can X take? Why is this a Poisson situation? What is the parameter?

b. What is the probability that exactly 7 left-handed people will be killed using a right-handed object tomorrow?

c. What is the expected number of left-handed people killed using a right-handed object over the next week?

d. What is the standard deviation of the number of left-handed people killed using a right-handed object over the next week?

e. What is the probability that at least 2 left-handed people will be killed using a right-handed object tomorrow?

f. What is the probability that you will have to check more than 3 days until you find the first day which has at least 2 left-handed people killed using a right-handed object? What distribution are you using now and what is the parameter?

Answer 1

a)

Since any number of people can be killed in this way so X can take values 0, 1, 2, 3, ....

Since we have average number of people killed in this way is a day (in a specific time frame) so X has Poisson distribution. Here X has Poisson distribution with parameter .

b)

The probability that exactly 7 left-handed people will be killed using a right-handed object tomorrow is

c)

Since one week means 7 days so here X has Poisson distribution with parameter

So the expected number of left-handed people killed using a right-handed object over the next week is

d)

The  standard deviation of the number of left-handed people killed using a right-handed object over the next week is

e)

f)

Here we need to use geometric distribution, let denoted by Y, with parameter p = 0.99169.

The probability that you will have to check more than 3 days until you find the first day which has at least 2 left-handed people killed using a right-handed object is