Answered

Standardized tests for certain subjects, given to high school students, are scored on a scale of 1 to 5. Let [tex]$X$[/tex] represent the score on a randomly selected exam. The distribution of scores for one subject's standardized test is given in the table.

\begin{tabular}{|c|c|c|c|c|c|}
\hline Score & 1 & 2 & 3 & 4 & 5 \\
\hline Probability & 0.18 & 0.20 & 0.26 & 0.21 & 0.15 \\
\hline
\end{tabular}

Which of the following is the correct interpretation of [tex]$P(X \ \textgreater \ 4)$[/tex]?

A. The probability of a randomly selected test having a score of at most 4 is 0.36.

B. The probability of a randomly selected test having a score of at least 4 is 0.36.

C. The probability of a randomly selected test having a score lower than 4 is 0.85.

D. The probability of a randomly selected test having a score higher than 4 is 0.15.



Answer :

GinnyAnswer
To determine the correct interpretation of [tex]\( P(X > 4) \)[/tex] using the given distribution of scores and their probabilities, we need to follow these steps:

1. Identify the possible scores and their corresponding probabilities:
- Score 1: Probability 0.18
- Score 2: Probability 0.20
- Score 3: Probability 0.26
- Score 4: Probability 0.21
- Score 5: Probability 0.15

2. Focus on the condition [tex]\( X > 4 \)[/tex]:
- A score greater than 4 can only be a score of 5 in this distribution.

3. Extract the probability of a score of 5:
- The probability of getting a score of 5 is 0.15.

Therefore, [tex]\( P(X > 4) \)[/tex] is 0.15.

With this information, let's analyze the given interpretations:

1. The probability of a randomly selected test having a score of at most 4 is 0.36.
- This is incorrect. The probability of scoring at most 4 includes the sum of the probabilities for scores 1, 2, 3, and 4.

2. The probability of a randomly selected test having a score of at least 4 is 0.36.
- This is incorrect. The probability of scoring at least 4 includes the sum of probabilities for scores 4 and 5.

3. The probability of a randomly selected test having a score lower than 4 is 0.85.
- This is incorrect. The probability of scoring lower than 4 includes the sum of probabilities for scores 1, 2, and 3.

4. The probability of a randomly selected test having a score higher than 4 is 0.15.
- This is correct. It directly matches the calculated probability for a score greater than 4.

Thus, the correct interpretation of [tex]\( P(X > 4) \)[/tex] is:

The probability of a randomly selected test having a score higher than 4 is 0.15.

Other Questions