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 probabilty distribution is right-skewed with a single peak at X = 10.

What is the shape of the probability distribution?

From the question, we have the following parameters that can be used in our computation:

Probability of blue, p = 0.80

Number of spin = 12

So, we have

Mean = 12 * 0.80

Mean = 9.6

And the standard deviation is

SD = √(9.6 * (1 - 0.8))

SD = 1.38

The graph is attached

And we have that the shape of the probability distribution is right-skewed with a single peak at x = 10