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

The shape of the probability distribution is approximately Normal with a single peak at X = 10.

Step-by-step explanation:

To make a graph of the probability distribution of X, we need to consider the number of times the spinner lands in the blue region out of 12 spins. Since the probability of landing in the blue region is 0.80, we can use the binomial distribution formula to calculate the probabilities for different values of X.

The shape of the probability distribution is determined by the values of X and their corresponding probabilities. In this case, as X ranges from 0 to 12, the probabilities will form a symmetric distribution with a peak at the most likely value. Since the probability of landing in the blue region is high (0.80), the distribution will be centered around this value and would have a single peak at X = 9.6 (0.80 * 12 = 9.6).

Therefore, the correct shape of the probability distribution is approximately Normal with a single peak at X = 10.