Questions: 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 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) Fewer than 3: (b) 4 or more: × 5

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 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) Fewer than 3:
(b) 4 or more:
×
5

Transcript text: 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 probabbility distribution of $X$. \begin{tabular}{|c|c|c|c|c|c|} \hline Value $\boldsymbol{x}$ of $\boldsymbol{X}$ & 1 & 2 & 3 & 4 & 5 \\ \hline $\boldsymbol{P}(\boldsymbol{X}=\boldsymbol{x})$ & 0.25 & 0.19 & 0.09 & 0.21 & 0.26 \\ \hline \end{tabular} For parts (a) and (b) below, find the probability that the randomly selected hair salon rating has the described number of stars. (a) Fewer than 3: $\square$ (b) 4 or more: $\square$ $\times$ 5

Solution

Solution Steps

Step 1: Identify the Range

Identify all $x_i < 3$.

Step 2: Sum Relevant Probabilities

Sum the probabilities of $X$ for all values that fall within the identified range. This involves adding up $P(X=x_i)$ for all $x_i$ that meet the condition. The sum of relevant probabilities is $\sum P(X=x_i) = 0.44$.