Question

An online spinner has two colored regions blue and yellow. According to the website, the probability that the spinner lands in the blue region on any spin is 0.80. Assume for now that this claim is correct. Suppose we spin the spinner 12 times and let X = the number of times it lands in the blue region.

Make a graph of the probability distribution of X. What is the shape of the probability distribution?

A) The shape of the probability distribution is left-skewed with a single peak at X = 10.

B) The shape of the probabilty distribution is right-skewed with a single peak at X = 8.

C) The shape of the probability distribution is approximately Normal with a single peak at X = 6.

D) The shape of the probabilty distribution is right-skewed with a single peak at X = 10.

E) The shape of the probabilty distribution is left-skewed with a single peak at X = 8.

Answer 1

A binomial distribution with 12 trials and a success probability of 0.80 is left-skewed with a single peak at X = 10, indicating that the most probable outcome is that the spinner will land on blue 10 times.

Step-by-step explanation:

The question concerns the probability distribution of X, the number of times a spinner lands in the blue region after spinning it 12 times. Given that the probability of landing in the blue region on any spin is 0.80, and assuming this probability is constant for each spin, X follows a binomial distribution with parameters n = 12 (the number of trials) and p = 0.80 (the probability of success on each trial).

To graph the probability distribution, we plot the number of successes (X) on the horizontal axis and the probability of each number of successes on the vertical axis. The peak of this distribution will be near the most likely number of successes, which can be calculated as n * p, and in this case is 12 * 0.80 = 9.6, which rounds to 10. Since the distribution is binomial and skewed towards the higher number of successes (due to a high probability of success on each trial), the correct answer is:

A) The shape of the probability distribution is left-skewed with a single peak at X = 10.