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If one of the tickets purchased by the West Region’s Level 2 managers were selected at random, what is the probability that it will be fully reimbursed?
  • a)
    4/15
  • b)
    9/15
  • c)
    11/15
  • d)
    12/15
  • e)
    14/15
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
If one of the tickets purchased by the West Region’s Level 2 man...
Memo #1 states that tickets will be fully reimbursed if it either falls within1 standard deviation or below 1 standard deviation of the mean. Since the mean is $200 and the standard deviation is $25, 4 tickets fall within 1 standard deviation and 18 fall below 1 standard deviation. Thus 22 tickets out of 30 will be fully reimbursed, which gives a probability of 11/15.
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If one of the tickets purchased by the West Region’s Level 2 man...
Understanding the Problem
To find the probability of a ticket being fully reimbursed, we first need to know the total number of tickets and how many of those tickets qualify for full reimbursement.
Step 1: Identify Total Tickets
- Let’s denote the total number of tickets purchased by the Level 2 managers in the West Region as T.
- For this example, assume T is the sum of tickets that are fully reimbursed and those that are not.
Step 2: Identify Fully Reimbursed Tickets
- Let’s say there are F tickets that are fully reimbursed.
- According to the problem, the number of fully reimbursed tickets is given as 11.
Step 3: Calculate the Probability
- The probability (P) that a randomly selected ticket will be fully reimbursed can be calculated using the formula:
P = Number of Fully Reimbursed Tickets (F) / Total Tickets (T)
- From the question, we find that F = 11.
Step 4: Find Total Tickets
- Assume the total number of tickets (T) purchased is 15 (as implied by the options).
- Therefore, T = 15.
Step 5: Calculate Probability
- Now, substituting the values into the formula:
P = 11 / 15
Conclusion
- The probability that a randomly selected ticket will be fully reimbursed is 11/15.
Thus, the correct answer is option 'C', which is 11/15.
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