91Ó°ÊÓ

Define the random variable X in words.

The random variable $X$is defined as follows:

$X=$the number of seniors who engaged in after-school sports over their entire high school career.

Make a list of the values that you want to use$\mathrm{X}$may be able to.

we see random variable $X$will be followed The value is given by, which has a binomial distribution and an upper bound of 60 is we get $x=0,1,2,…,60$.

The distribution we have $\mathrm{X}~\mathrm{X}$.

Binomial distribution will be applied to the random variable$X.$

$X~B(60,0.08)$

The expected Binomial distribution is calculated as follows:

$\mathrm{μ}=np$

$\mathrm{μ}=60×0.08$

$\mathrm{μ}=4.8$

As a result, $4.8$seniors are anticipated to have participated in after-school sports during their four years of high school.

The required probability can be expressed as $P(x=0)$than it calculated by calculator.

As a result, $P(x=0)=0.00671$Because the likelihood of none of the seniors participating in after-school sports all four years of high school is quite low, it will come as a surprise if none of the seniors participate in after-school sports all four years of high school.

It's possible to write the requisite probability as,

$P(x=4)\text{and}P(x=5)$

Than it is calculated by using $Ti-83$using calculator.

$P(x=4)$

$.1873152554$

$P(x=5)$

$.1824287705$

As a result, when $P(x=4)$ and $P(x=5)$ are compared, it is more likely that four or five of the seniors participated in after-school sports throughout their four years of high school.