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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 stars of the selected rating. Here is the probability distribution of 
X.




Value 
x of 
X
1
2
3
4
5



P(X=x)
0.25
0.19
0.09
0.21
0.26




For parts (a) and (b) below, find the probability that the randomly selected hair salon rating has the described number of stars.
(a) At most 2:
(b) More than 3:

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22\newline33\newline44\newline55\newline66\newline77\newline88\newline99\newline1010\newline1111\newline1212\newlineOn a popular app, users rate hair salons as 1,2,3,4 1,2,3,4 , or 55 stars. Suppose a rating is randomly selected from all the ratings on the app. Let X X be the number stars of the selected rating. Here is the probability distribution of X X .\newline\begin{tabular}{|c|c|c|c|c|c|}\newline\hline Value x x of X X & 11 & 22 & 33 & 44 & 55 \\\newline\hlineP(X=x) P(X=x) & 00.2525 & 00.1919 & 00.0909 & 00.2121 & 00.2626 \\\newline\hline\newline\end{tabular}\newlineFor parts (a) and (b) below, find the probability that the randomly selected hair salon rating has the described number of stars.\newline(a) At most 22:\newline(b) More than 33:\newline \square

Full solution

Q. 22\newline33\newline44\newline55\newline66\newline77\newline88\newline99\newline1010\newline1111\newline1212\newlineOn a popular app, users rate hair salons as 1,2,3,4 1,2,3,4 , or 55 stars. Suppose a rating is randomly selected from all the ratings on the app. Let X X be the number stars of the selected rating. Here is the probability distribution of X X .\newline\begin{tabular}{|c|c|c|c|c|c|}\newline\hline Value x x of X X & 11 & 22 & 33 & 44 & 55 \\\newline\hlineP(X=x) P(X=x) & 00.2525 & 00.1919 & 00.0909 & 00.2121 & 00.2626 \\\newline\hline\newline\end{tabular}\newlineFor parts (a) and (b) below, find the probability that the randomly selected hair salon rating has the described number of stars.\newline(a) At most 22:\newline(b) More than 33:\newline \square
  1. Calculate Probability for 22 Stars: To find the probability of a rating being at most 22 stars, we add the probabilities of getting 11 star and 22 stars.\newlineCalculation: P(X=1)+P(X=2)=0.25+0.19P(X=1) + P(X=2) = 0.25 + 0.19
  2. Evaluate Sum for 22 Stars: Evaluate the sum of the probabilities for at most 22 stars. 0.25+0.19=0.440.25 + 0.19 = 0.44
  3. Calculate Probability for More than 33 Stars: To find the probability of a rating being more than 33 stars, we add the probabilities of getting 44 stars and 55 stars.\newlineCalculation: P(X=4)+P(X=5)=0.21+0.26P(X=4) + P(X=5) = 0.21 + 0.26
  4. Evaluate Sum for More than 33 Stars: Evaluate the sum of the probabilities for more than 33 stars. 0.21+0.26=0.470.21 + 0.26 = 0.47

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