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Hi Scott how many more math classes will I have to endure,

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Hi Scott how many more math classes will I have to endure, I really aperichate the help you have gave me and I am back statistiWeek 4 Quiz (Due Friday Jun 18, 2010)
Posted: Sun 06/13/2010 08:10 AM , by: Pam Bennett ([email protected] )
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Week Four Quiz



1. Which of the following statements are correct?

A normal distribution is any distribution that is not unusual.
The graph of a normal distribution is bell-shaped.
If a population has a normal distribution, the mean and the median are not equal.
The graph of a normal distribution is symmetric.


Using the 68-95-99.7 rule:

Assume that a set of test scores is normally distributed with a mean of 100 and a standard deviation of 20. Use the 68-95-99.7 rule to find the following quantities:

Suggest you make a drawing and label first…

Percentage of scores less than 100
Relative frequency of scores less than 120
Percentage of scores less than 140
Percentage of scores less than 80
Relative frequency of scores less than 60
Percentage of scores greater than 120


2. Assume the body temperatures of healthy adults are normally distributed with a mean of 98.20 °F and a standard deviation of 0.62 °F (based on data from the University of Maryland researchers).

If you have a body temperature of 99.00 °F, what is your percentile score?
Convert 99.00 °F to a standard score (or a z-score).
Is a body temperature of 99.00 °F unusual? Why or why not?
Fifty adults are randomly selected. What is the likelihood that the mean of their body temperatures is 97.98 °F or lower?
A person’s body temperature is found to be 101.00 °F. Is the result unusual? Why or why not? What should you conclude?
What body temperature is the 95th percentile?
What body temperature is the 5th percentile?
Bellevue Hospital in New York City uses 100.6 °F as the lowest temperature considered to indicate a fever. What percentage of normal and healthy adults would be considered to have a fever? Does this percentage suggest that a cutoff of 100.6 °F is appropriate?cal reasoning, can you help? here it is
Submitted: 8 years ago.Category: Math Homework
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6/14/2010
Math Tutor or Teacher: Scott, MIT Graduate replied 8 years ago
Scott
Scott, MIT Graduate
Category: Math Homework
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Hey Sidney, math is fun! Hopefully you'll be in a lot more math classes, because I enjoy helping you out :)


1. Which of the following statements are correct?
A normal distribution is any distribution that is not unusual.
FALSE, it's a bell shaped distribution.


The graph of a normal distribution is bell-shaped.
TRUE, by definition


If a population has a normal distribution, the mean and the median are not equal.
FALSE, they are equal


The graph of a normal distribution is symmetric.
TRUE, by definition

 

Using the 68-95-99.7 rule: Assume that a set of test scores is normally distributed with a mean of 100 and a standard deviation of 20.
Use the 68-95-99.7 rule to find the following quantities: Suggest you make a drawing and label first...
Percentage of scores less than 100
drawing:


less than the mean is:
50%


Relative frequency of scores less than 120
120 is 1 stdev above the mean.
32% is outside 1 stdev, but only 16% (half) is above 1 stdev.
1 - 0.16
= 0.84


Percentage of scores less than 140
140 is 2 stdevs above the mean.
5% is outside 2 stdevs, but only 2.5% (half) is above 2 stdevs.
100% - 2.5%
= 97.5%


Percentage of scores less than 80
80 is 1 stdev below the mean.
32% is outside 1 stdev, but only 16% (half) is below 1 stdev.
so the answer is:
16%


Relative frequency of scores less than 60
60 is 2 stdevs below the mean.
5% is outside 2 stdevs, but only 2.5% (half) is below 2 stdevs.
so the answer is:
0.025


Percentage of scores greater than 120
This is 100% - the answer to "less than 120"
= 16%

 

2. Assume the body temperatures of healthy adults are normally distributed with a mean of 98.20 °F and a standard deviation of 0.62 °F (based on data from the University of Maryland researchers). If you have a body temperature of 99.00 °F, what is your percentile score?
z = (99-98.2)/0.62

z = 1.29

percentile(z=1.29) from the table is:

0.9015

= 90.15%

 

b. Convert 99.00 °F to a standard score (or a z-score).

z = (99-98.2)/0.62

z = 1.29

 

c. Is a body temperature of 99.00 °F unusual? Why or why not?

Yes, it's unusual. Temperatures of 99 or higher only happen about 10% of the time.

 

d. Fifty adults are randomly selected. What is the likelihood that the mean of their body temperatures is 97.98 °F or lower?

z = (x-mu)/(sigma/sqrt(N))

z = (97.98-98.2)/(0.62/sqrt(50))

z = -2.509

prob(z < -2.509)

= 0.0061

 

e. A person's body temperature is found to be 101.00 °F. Is the result unusual? Why or why not? What should you conclude?

z = (101-98.2)/0.62

z = 4.516

prob(z > 4.516)

= about 0

This is very unusual, since almost none of the curve lies above 101.

 

f. What body temperature is the 95th percentile?

z(95%) = 1.6449

x = mu + z*sigma

x = 98.2 + 1.6449*0.62

x = 99.22 deg

 

g. What body temperature is the 5th percentile?

z(5%) = -1.6449

x = mu + z*sigma

x = 98.2 - 1.6449*0.62

x = 97.18 deg

 

h. Bellevue Hospital in New York City uses 100.6 °F as the lowest temperature considered to indicate a fever. What percentage of normal and healthy adults would be considered to have a fever? Does this percentage suggest that a cutoff of 100.6 °F is appropriate?

z = (100.6-98.2)/0.62

z = 3.87

prob(z > 3.87)

= 0.0001

= 0.01%

This is a good cutoff, since very very few normal adults will be considered to have a fever.

 

Let me know if you have any questions,
Scott

Scott
Scott, MIT Graduate
Category: Math Homework
Satisfied Customers: 17,710
Experience: Over 13,000 accepts & 100% feedback in the old math category
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Scott and 87 other Math Homework Specialists are ready to help you
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Customer reply replied 8 years ago
scott you are great but I repect math but I don't like it and it has enabled me to meet a new friend, you are great Sidney
Math Tutor or Teacher: Scott, MIT Graduate replied 8 years ago

Glad to help!

-Scott

Ask Your Own Math Homework Question
Customer reply replied 7 years ago
Scott are you still there i just asked a question for math and they sent it to a lawyer is there anyway you can help me this is Sidney
Math Tutor or Teacher: Scott, MIT Graduate replied 7 years ago

Hey, I see the question, but I'm afraid that it's Business/Finance, and not math :(

-Scott

Ask Your Own Math Homework Question
Customer reply replied 7 years ago
And who would I direct that to sorry to bother you its not a lawyer is it, can I re submitt
Math Tutor or Teacher: Scott, MIT Graduate replied 7 years ago

You can post in the Business Homework category. If you want to ask for a specific person, try Neo or BusinessTutor.

-Scott

Ask Your Own Math Homework Question
Customer reply replied 7 years ago
Thanks Scott you are the best
Math Tutor or Teacher: Scott, MIT Graduate replied 7 years ago

Thanks! And if you have any more math in the future, please do let me know!

-Scott

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