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 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? (For the answer to question 14, 15, and 16, start with making a bell curve. Identify on the bell curve where is mean, X, and area(s) to be determined. 14. What percent of the refunds are more than $3,500? 15. What percent of the refunds are more than $3500 but less than $3579? 16. 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 normal distribution. The mean of the distribution is 15.0 minutes and the standard deviation is 3.5 minutes. What is the probability that a particular listener will tune in for: 17. More than 20 minutes? 18. 20 minutes or less? 19. Between 10 and 12 minutes? 20. Between 15 and 20 minutes? (this part is not from the textbook)

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter4: Polynomial And Rational Functions

Section4.6: Rational Functions

Problem 11SC: Find the mean hourly cost when the cell phone described above is used for 240 minutes.

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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.

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

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? (For the answer to question 14, 15, and 16,
start with making a bell curve. Identify on the bell curve where is mean, X, and area(s) to be determined.
14. What percent of the
refunds are more than
$3,500?
15. What percent of the
refunds are more than
$3500 but less than $3579?
16. 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 normal distribution. The mean of the distribution is 15.0
minutes and the standard deviation is 3.5 minutes. What is the probability that a particular
listener will tune in for:
17. More than 20 minutes?
18. 20 minutes or less?
19. Between 10 and 12
minutes?
20. Between 15 and 20
minutes? (this part is not
from the textbook)

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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