Question

The probability that Pete will catch fish on a particular day when he goes fishing is .8. Peter is going fishing 3 days. The variance of the number of days Pete will catch fish isa. .48b. .8c. 2.4d. .16

Answer 1

`Var(X) = np(1-p) = 3*0.8*(1-0.8) = 0.48`

And the standard deviation for the random variable is given by:

`sd(X)=√(np(1-p))=√(3*0.8*(1-0.8))=0.693`

So the correct option for this case would be:

0.48

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Solution to the problem

Let X the random variable of interest "number of days Pete will catch fish", on this case we now that:

`X \sim Binom(n=3, p=0.8)`

The probability mass function for the Binomial distribution is given as:

`P(X)=(nCx)(p)^x (1-p)^(n-x)`

Where (nCx) means combinatory and it's given by this formula:

`nCx=(n!)/((n-x)! x!)`

The expected value is given by this formula:

`E(X) = np=3*0.8=2.4`

The variance for the random variable X is given by:

`Var(X) = np(1-p) = 3*0.8*(1-0.8) = 0.48`

And the standard deviation for the random variable is given by:

`sd(X)=√(np(1-p))=√(3*0.8*(1-0.8))=0.693`

So the correct option for this case would be:

0.48