Using the binomial distribution, it is found that the spinner is expected to have to spin approximately 132 times for a multiple of 5 to be spun 22 times, hence option 4 is correct.
What is the binomial probability distribution?
It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.
The expected number of trials until q successes is:
[tex]E_f(X) = \frac{q}{p}[/tex]
In this problem:
- We want 22 successes, hence q = 22.
- 2 out of 12 sections(5 and 10) are multiples of 5, hence p = 1/6.
Then:
[tex]E_f(X) = \frac{q}{p} = \frac{22}{\frac{1}{6}} = 22 \times 6 = 132[/tex]
Hence option 4 is correct.
More can be learned about the binomial distribution at https://brainly.com/question/14424710
