Question

Taking the train Refer to Exercise 80 . Use the binomial probability formula to find $P(Y=$$4)$. Interpret this value.

Short answer

On selected days, there's a chance that 4 out of 7 trains will be late $9.84\%$

Step-by-step solution

Given Information

The total number of trials $\left(n\right)=6$

The likelihood of success ( p) $=0.90$

The binomial probability is calculated using the following formula:

$P(X=r)={}^{n}C_r\times p^r\times (1-p{)}^{n-r}$

Furthermore,

The number of successes is r in this case.

The number of trials is n.

The chance of success is denoted by p.

Simplification

Assume, $\mathrm{Y}$that is a random variable that follows a binomial distribution$\mathrm{n}=6$and $p=0.90$.

$P(Y=4)$ can be computed as follows:

$=0.0984$

As a result, the necessary probability is$0.0984.$

On selected days, there's a chance that four out of seven trains will arrive late is $9.84\%$