Question No Mean Q 11 Std. dev. X Result reater/Less/Betwee Answer 50 4 44 50 4 55 Q12 50 st Between 44-55 4 55 Greater than 55 Q13 50 4 52 50 4 55 Between 52-55 Q14 3401 82.5 3500 More than 3500 Q15 3401 82.5 3500 3401 82.5 3579 Between 3500-3579 Q16 3401 82.5 3325 3401 82.5 3579 Between 3325-3579 Q17 15 3.5 20 More than 20 Q18 15 3.5 20 Less than 20 Q19 15 3.5 10 15 3.5 12 Between 10-12 Q20 15 3.5 15 15 3.5 20 Between 15-20
In order to find probability, you can use this formula in Microsoft Excel:
- The best way to understand and solve these problems is by first drawing a bell curve and marking key points such as x, the mean, and the areas of interest. Once marked on the bell curve, figure out what calculations are needed to find the area of interest.
- =NORM.DIST(x, Mean, Standard Dev., TRUE).
- When the question mentions “greater than” you may have to subtract your answer from 1.
- When the question mentions “between (two values)”, you need to do separate calculation for both values and then subtract their results to get the answer.
1.
- Compute the probability of a value between 44.0 and 55.0.
(The question requires finding probability value between 44 and 55. Solve it in 3 steps.
- In the first step, use the above formula and x = 44, calculate probability value.
- In the second step repeat the first step with the only difference that x=55.
In the third step, subtract the answer of the first part from the answer of the second part.)
2. Compute the probability of a value greater than 55.0.
Use the same formula, x=55 and subtract the answer from 1.
3. Compute the probability of a value between 52.0 and 55.0.
(The question requires finding probability value between 52 and 55. Solve it in 3 steps.
- In the first step, use the above formula and x = 52, calculate probability value.
- In the second step repeat the first step with the only difference that x=55.
In the third step, subtract the answer of the first part from the answer of the second part.)
Suppose the Internal Revenue Service reported that the mean tax refund for the year 2022 was $3401. Assume the standard deviation is $82.5 and that the amounts refunded follow a normal probability distribution. Solve the following three parts?
What percent of the refunds are more than $3,500?
What percent of the refunds are more than $3500 but less than $3579?
What percent of the refunds are more than $3325 but less than $3579?
WNAE, an all-news AM station, finds that the distribution of the lengths of time listeners are tuned to the station follows the
More than 20 minutes?
20 minutes or less?
Between 10 and 12 minutes?
Between 15 and 20 minutes? (this part is not from the textbook)
Step by step
Solved in 2 steps
