Answer:
The estimated number of times the spinner will land on 3 is 20.
Step-by-step explanation:
The complete question is:
A four-sided spinner is provided. If Tom spins the spinner 80 times then work out an estimate for the number of times the spinner will land on 3.
Solution:
Assume that the four-sided spinner is unbiased.
That is all the four outcomes are equally likely to be selected.
The probability that the spinner lands on any of the four numbers is:
P(1) = P (2) = P (3) = P (4) = 0.25
It is provided that Tom spins the spinner n = 80 times.
The spinner can land on any of the four numbers independently.
The random variable X, defined as the number of times the spinner lands on 3, follows a Binomial distribution with parameters n = 80 and p = 0.25.
The expected value of X is:
[tex]E(X)=np[/tex]
[tex]=80\times 0.25\\=20[/tex]
Thus, the estimated number of times the spinner will land on 3 is 20.
