Question

A random sample of 40 hotel reviews is drawn from a large population of hotel customers. It's known that 30% of the population left the hotel 1 star, 20% left 2 stars, 20% left 3 stars, and 30% left 4 stars. Give the standard deviation of the hotel's star rating.

Answer 1

Here we see that and also all probabilities are between 0 to 1. Hence all the properties of probabilities are satisfied.

So the probability table is

x	P(x)
1	0.3
2	0.2
3	0.2
4	0.3

To find standard deviation we need to find mean first

Now we need to find

So standard deviation is

So the standard deviation of the hotel's star rating is 1.2042