Suppose that it is known that 10 percent of a certain population is color

blind. If a random sample of 20 people is drawn from this population, answer the

following:

(a) What is the probability of ve or fewer are color blind?

(b) What is the probability that 6 or more will be color blind?

(c) What is the probability between 6 and 9, inclusive will be color blind? (must use

2 commands in R to get the answer and adding them is not the answer, you will

need to subtract them!)

(d) What is the probability that two, three or four will be color blind? (must use 2

commands in R to get the answer and adding them is not the answer, you will

need to subtract them!)

R Assistance

1. To compute Pr(X = x) using the binomial with n trials and p, the probability of

success, use the command dbinom(x,n,p) at the R prompt. For example, Pr(X = 3)

with n = 5; p = 0:6 is dbinom(3,5,0.6) = 0.3546.

2. To compute the Pr(X x) using the binomial with n trials and p, the probability of

success, use the command pbinom(x,n,p) at the R prompt. For example, Pr(X 3)

with n = 5; p = 0:6 is pbinom(3,5,0.6) = 0.66304.

3. To nd Pr(X > x) you can use the complement of 1 Pr(X x) and the above

commands.

4. To compute Pr(X = x) using the Poisson with average rate of success, use the

command dpois(x,mu) at the R prompt. For example, Pr(X = 3) with = 5 is

dpois(3,5) = 0.1403739.

5. To compute the Pr(X x) using the Poisson with average rate of success, use

the command ppois(x,mu) at the R prompt. For example, Pr(X 3) with = 5 is

ppois(3,5) = 0.2650259.

6. To nd Pr(X > x) you can use the complement of 1 Pr(X x) and the above

commands.