Question

random variables and distributions
discrete probability distribution: word problem involving cumulative...
on a popular app, users rate restaurants 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.

for parts (a) and (b) below, find the probability that the randomly selected restaurant rating has the described number of stars.
(a) fewer than 4:
(b) 3 or more:

Explanation:

Step1: Calculate probability for fewer than 4

Fewer than 4 means \(x = 1\), \(x=2\), \(x = 3\).
Use \(P(X<4)=P(X = 1)+P(X = 2)+P(X = 3)\)
\(P(X<4)=0.22 + 0.19+0.11\)
\(P(X<4)=0.52\)

Step2: Calculate probability for 3 or more

3 or more means \(x = 3\), \(x=4\), \(x = 5\).
Use \(P(X\geq3)=P(X = 3)+P(X = 4)+P(X = 5)\)
\(P(X\geq3)=0.11+0.25 + 0.23\)
\(P(X\geq3)=0.59\)

Answer:

(a) \(0.52\)
(b) \(0.59\)