Question

a.) For desktops, the current market share for Windows is 79%. If the operating systems are checked for 20 randomly selected desktops, what is the probability that 17 of them are running Windows? Answer this question without using R or a binomial calculator function. I want you to simplify the combination manually, but a calculator can certainly be used to multiply the combination by ?? ∙(?−?)?−?.
b.) A certain drug treatment cures 90% of cases of hookworm in children. Suppose 50 children suffering from hookworm are to be treated, and all of them receive the treatment. Find the probability that at least 40 are cured.   Answer this question using the pbinom function in R. The command typed into R can either be included as a screenshot or written out by hand.



c.) In California, about 10% of all homeowners are insured against earthquake damage. 30 homeowners are to be selected at random; let X denote the number among the 30 who have earthquake insurance. What is the probability that 3 or less of the 30 selected have earthquake insurance?   Answer this question using the pbinom function in R. The command typed into R can either be included as a screenshot or written out by hand.

Answer 1

a) The probability that For desktops, the current market share for Windows is p=0.79

Let X be the number of desktops running Windows.

Therefore,

The probability that 17 of them are running Windows is given by:

b) The probability that the certain drug treatment cures cases of hookworm in children is p=0.90

Let X be the number of cases of hookworm in children cured by certain drug.

Therefore,

The probability that at least 40 are cured given by:

By usinr R command:

> pbinom(39,50,0.90)
[1] 0.009354602

c) The probability of all homeowners are insured against earthquake damage given by:

p=0.10

let X denote the number among the 30 who have earthquake insurance.

Therefore,

The probability that 3 or less of the 30 selected have earthquake insurance is given by:

### By using R command:

> pbinom(3,30,0.10)
[1] 0.6474392