Question

Taking the train According to New Jersey Transit, the $8:00$A.M. weekday train from Princeton to New York City has a $90\%$chance of arriving on time on a randomly selected day. Suppose this claim is true. Choose 6 days at random. Let localid="1654594369074" $\mathrm{Y}=$the number of days on which the train arrives on time.

Short answer

The given statement is true, because Y is followed by binomial distribution

Step-by-step solution

Given Informaiotn

The likelihood of success $\left(\mathrm{p}\right)=90\%=0.90$

The number trials conducted $\left(\mathrm{n}\right)=6$

Simplification

The random variable Y satisfies the following requirements.

1. The likelihood of success, i.e., the probability of arriving on time, is fixed at 0.90.

2. The number of days is set.

3. Days are separate from one another.

4. There are two possible outcomes: trains arriving on time or not arriving on time.

Here, all of the binomial criteria are met. As a result, Y is said to follow the binomial distribution.