On a popular app, users rate hair salons as 1, 2, 3, 4, or 5 stars. Suppose a rating is randomly selected from all the ratings on the app. Let X be the number of stars of the selected rating. Here is the probability distribution of X.Value x of X 1 2 3 4 5P=Xx 0.24 0.20 0.09 0.20 0.27For parts (a) and (b) below, find the probability that the randomly selected hair salon rating has the described number of stars.(a) 4 or more:(b) Fewer than 3:
Question
On a popular app, users rate hair salons as 1, 2, 3, 4, or 5 stars. Suppose a rating is randomly selected from all the ratings on the app. Let X be the number of stars of the selected rating. Here is the probability distribution of X.Value x of X 1 2 3 4 5P=Xx 0.24 0.20 0.09 0.20 0.27For parts (a) and (b) below, find the probability that the randomly selected hair salon rating has the described number of stars.(a) 4 or more:(b) Fewer than 3:
Solution
(a) To find the probability that the randomly selected hair salon rating has 4 or more stars, we need to add the probabilities of getting 4 and 5 stars.
From the given probability distribution, P(X=4) = 0.20 and P(X=5) = 0.27.
So, P(X>=4) = P(X=4) + P(X=5) = 0.20 + 0.27 = 0.47.
(b) To find the probability that the randomly selected hair salon rating has fewer than 3 stars, we need to add the probabilities of getting 1 and 2 stars.
From the given probability distribution, P(X=1) = 0.24 and P(X=2) = 0.20.
So, P(X<3) = P(X=1) + P(X=2) = 0.24 + 0.20 = 0.44.
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