Description
3. In the sample given on the data tab, 285 of the 599 jobs have an average salary greater than $60,000. Test the claim that more than 45% of the jobs have an average salary greater than $60,000 using a 0.05 significance level. for spread sheets
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Instructions: The following questions on the next six tabs are shown to you by a student who is asking for help. Your job is
by showing the student how to solve each problem in detail. You are expected to explain all of the steps in your own words
Key:
– This problem is an incorrect. Your job is to find the errors, correct the errors, and explain what they did wrong.
– This problem is partially finished. You must complete the problem by showing all steps and explain your corrections
– This problem is blank. You must start from scratch and explain how you will approach the problem, how you solve it,
sking for help. Your job is to help the student walk through the problems
e steps in your own words.
hat they did wrong.
explain your corrections.
roblem, how you solve it, and explain why you took each step.
The average daily temperature in Orlando, Florida during the month of January follows a normal distribution w
of 60°F and a standard deviation of 5°F. What percentage of days in January, will the temperature be less than 57
Orlando?
Show your calculations using Excel functions in the area to the right of this text box and answer the problem with expl
below.
Given mean standard deviation and X. We use excel function NORMDIST(x,mean,standard deviation,TRUE)
p value = 0.2743
in percentage
=27.43%
The percentage of days in January the temperature in Orlando will be less than 57F is 27.43%
Normal Distribution: The problem states that the daily temperature in Orlando during January follows a normal distri
normal distribution is a type of continuous probability distribution for a real-valued random variable. It is symmetric a
mean, showing that data near the mean are more frequent in occurrence than data far from the mean.
Mean: The mean temperature is given as 60°F. This is the “center” of the normal distribution, and in the context of th
it’s the average temperature for January.
Standard Deviation: The standard deviation is given as 5°F. This measures the amount of variation or dispersion of tem
from the mean. A smaller standard deviation indicates that the temperatures are closer to the mean, while a larger o
that the temperatures are more spread out.
The Specific Temperature (X): We’re interested in the temperature of 57°F.
Cumulative Distribution Function (CDF): The Excel function NORMDIST(x, mean, standard deviation, TRUE) is used to
cumulative probability up to a point, which is the CDF. In this context, it tells us the probability that the temperature
randomly selected day in January will be less than 57°F.
Calculation of p-value: When you use the NORMDIST function with the parameters (57, 60, 5, TRUE), it calculates the
the curve of the normal distribution to the left of 57°F. This area represents the probability (p-value) that the temper
less than 57°F.
Interpretation of p-value: The p-value of 0.2743, or 27.43% when converted to a percentage, tells us that there is a 27
that on any given day in January, the temperature in Orlando will be less than 57°F.
Percentage of Days: Since January typically has 31 days, we can infer that approximately 27.43% of those days (which
about 8.5 days, if we multiply 0.2743 by 31) will have temperatures less than 57°F.
This kind of analysis is useful for planning purposes in sectors like agriculture, tourism, and logistics, where temperatu
a significant impact on operations.
ws a normal distribution with a mean
perature be less than 57°F in
wer the problem with explanations
X
mu
sd
57
60
5
z
-0.6
deviation,TRUE)
P
ary follows a normal distribution. A
m variable. It is symmetric about the
m the mean.
n, and in the context of this problem,
riation or dispersion of temperatures
the mean, while a larger one indicates
eviation, TRUE) is used to calculate the
lity that the temperature on a
5, TRUE), it calculates the area under
value) that the temperature will be
e, tells us that there is a 27.43% chance
.43% of those days (which would be
logistics, where temperature can have
0.274253
The weight of boxes of Cheerios are normally distributed with a mean of 15.3 ounces with a standard deviation
ounces. Find the probability that a randomly selected box of Cheerios will weigh more than 16 ounces.
Show your calculations using Excel functions in the area to the right of this text box and answer the problem with expl
below.
Given mean standard deviation and X. We use excel function NORMDIST(x,mean,standard deviation,TRUE)
p value = 0.0599
in percentage
=59.9%
The percentage that the selectrd box weigh more thani 16 ounce is 59.9%
The result obtained, approximately 0.0594 or 5.94% when expressed as a percentage, signifies the probability that a r
selected box of Cheerios will weigh more than 16 ounces. This probability is derived from the normal distribution with
15.3 ounces and a standard deviation of 0.45 ounces. In essence, there is about a 5.94% chance that a randomly chos
exceed the weight of 16 ounces, based on the given distribution parameters.
with a standard deviation of 0.45
an 16 ounces.
wer the problem with explanations
deviation,TRUE)
fies the probability that a randomly
he normal distribution with a mean of
ance that a randomly chosen box will
X
mu
sd
16
15.3
0.45
pvalue
0.940093
Right tailed=10.059907
Assume that a randomly selected subject is given a bone density test. Those tests follow a standard normal
distribution. Find the probability that the bone density score for this subject is between -1.24 and 0.33.
Show your calculations using Excel functions in the area to the right of this text box and answer the problem with
explanations below.
=0.6293-0.1075
=0.5218
The probability is 0.5218
The result obtained, approximately 0.0599 or 5.99% when expressed as a percentage, represents the probability that
randomly selected box of Cheerios will weigh more than 16 ounces.
In other words, there is a 5.99% chance that a randomly selected box of Cheerios will have a weight exceeding 16 oun
given that the weights of Cheerios boxes are normally distributed with a mean of 15.3 ounces and a standard deviatio
0.45 ounces.
This probability is obtained by calculating the area under the normal distribution curve to the right of the value of 16
ounces. Since the normal distribution is symmetric, we can use the complement rule: subtracting the probability of th
event “weight less than or equal to 16 ounces” from 1, to find the probability of the event “weight more than 16 oun
Therefore, the probability that a randomly selected box of Cheerios will weigh more than 16 ounces is approximately
5.99%.
ow a standard normal
1.24 and 0.33.
wer the problem with
esents the probability that a
a weight exceeding 16 ounces,
es and a standard deviation of
he right of the value of 16
acting the probability of the
weight more than 16 ounces.”
6 ounces is approximately
)
0.107488
0.6293
Women’s pulse rates are normally distributed with a mean of 78 beats per minute and a standard deviation of
minute. What is the z-score for a woman having a pulse rate of 71 beats per minute?
Student’s incorrect answer:
Let =
−
=
( − )
.
= .
Identify where the student went wrong when solving the problem above. Show how to correctly calculate the answer
the cells to the right of this text box. Finish the problem by stating how to correctly set up the problem and solve it bel
The student keyed the wrong value in the formula.
x is 71 not 78
z=(71-78)/9.8
=-0.71
The correct answer is -0.71
=
d a standard deviation of 9.8 beats per
ectly calculate the answer using Excel in
e problem and solve it below.
What is the cumulative area from the left under the curve for a z-score of -1.55? What is the area on the right o
score? Hint: You will have two answers (one for the left and one for the right).
Student’s partially finished answer:
The first part is to find the cumulative area from the left under the curve for a z-score of -1.55. This means that I ne
the probability that a z-score is less than -1.55.
Show your calculations using Excel functions in the cells to the right of this text box and finish answering the problem w
explanations below.
area to the left
pvalue =0.0606
The area to the left is 0.0606
area to the right is
1-0.0606=0.9393
The area to the right is 0.9393
The results indicate the cumulative probability associated with a z-score of -1.55 in a standard normal distribution.
•The area to the left of the z-score (-1.55) represents the probability that a randomly selected value from the standar
distribution is less than -1.55 standard deviations from the mean. In this case, it’s approximately 0.0606 or 6.06%.
•The area to the right of the z-score (-1.55) represents the probability that a randomly selected value from the standa
distribution is greater than -1.55 standard deviations from the mean. In this case, it’s approximately 0.9394 or 93.94%
These results provide insights into the distribution of values relative to the mean in a standard normal distribution.
t is the area on the right of that z-
1.55. This means that I need to find
h answering the problem with
ard normal distribution.
ed value from the standard normal
ately 0.0606 or 6.06%.
cted value from the standard normal
ximately 0.9394 or 93.94%.
ard normal distribution.
0.060571
If the area under the standard normal distribution curve is 0.2643 from the right, what is the corresponding z
Student’s incorrect answer:
We plug in “=NORM.S.INV(0.2643)” into Excel and get a z-score of -0.63.
Identify where the student went wrong when solving the problem above. Show how to correctly calculate the answer
the cells to the right of this text box. Finish the problem by stating how to correctly set up the problem and solve it bel
since the data is rght skewed
1-0.2643
=0.7357
=0.63
t is the corresponding z-score?
ectly calculate the answer using Excel in
e problem and solve it below.
0.630145
Job Title
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Technical Writers
Telecommunications Equipment Installers and Repairers, Except Line Installers
Telecommunications Line Installers and Repairers
Telemarketers
Tellers
Textile Knitting and Weaving Machine Setters, Operators, and Tenders
Therapists, All Other
Title Examiners, Abstractors, and Searchers
Tool and Die Makers
Tool Grinders, Filers, and Sharpeners
Training and Development Managers
Training and Development Specialists
Transit and Railroad Police
Transportation and Material Moving Occupations
Transportation Inspectors
Transportation, Storage, and Distribution Managers
Travel Agents
Tutors and Teachers and Instructors, All Other
Umpires, Referees, and Other Sports Officials
Underground Mining Machine Operators and Extraction Workers, All Other
Upholsterers
Urban and Regional Planners
Veterinarians
Veterinary Technologists and Technicians
Water and Wastewater Treatment Plant and System Operators
Web Developers and Digital Interface Designers
Weighers, Measurers, Checkers, and Samplers, Recordkeeping
Welders, Cutters, Solderers, and Brazers
Welding, Soldering, and Brazing Machine Setters, Operators, and Tenders
Wind Turbine Service Technicians
Woodworkers, All Other
Woodworking Machine Setters, Operators, and Tenders, Except Sawing
Word Processors and Typists
Writers and Authors
Zoologists and Wildlife Biologists
Yearly Average Salary
76,130
112,030
80,390
39,460
112,420
58,860
122,770
51,930
115,910
65,160
41,570
38,540
59,800
100,480
37,230
132,220
55,100
79,080
31,380
31,380
45,440
70,410
39,580
74,440
84,040
100,650
57,170
152,910
84,810
47,820
86,380
111,960
101,350
47,680
57,790
164,800
53,660
87,970
87,730
49,970
89,780
52,730
51,390
44,420
46,780
66,350
Calculations/Values
Mean
Standard Deviation
n
Formulas/Answers
65,081
27290.903
599
52,770
33,750
42,630
33,250
43,090
43,790
110,240
84,010
75,860
46,510
85,170
44,960
71,450
62,060
33,510
40,130
56,660
81,270
35,320
53,700
44,050
80,310
111,630
35,790
71,920
42,620
62,510
46,030
52,340
76,860
66,690
72,630
72,500
64,540
56,250
54,990
60,830
70
