Download Problem of the Day If you get an 87% on a test, what grade should

Problem of the Day
If you get an 87% on a test, what grade should you get and why?
Problem of the Day
Men's combined skiing employs a downhill portion and a slalom portion. The mean for the downhill was 101.807 seconds with a standard deviation of 1.8356. The mean for the slalom portion was 94.2714 with a standard deviation of 5.2844. Suppose you won the race with a combined time of 189.35 seconds, 101.42 in the downhill and 87.93 in the slalom. Which was your better race?
Problem of the Day
Beanstalk Clubs are social clubs for tall people. Men must be over 6’2” and women must be over 5’10”. National Health surveys show men’s heights are normally distributed with a mean of 69.1 inches and a standard deviation of 2.8 inches. Women’s heights are normally distributed with a mean of 64 inches and a standard deviation of 2.5 inches.
Who are more likely to qualify for the Beanstalk Club, men or women? Why?
Problem of the Day
Which of the following variables would most likely follow a Normal model?
A) family income B) heights of singers in a co­ed choir
C) weights of adult male elephants D) scores on an easy test
E) all of these
Problem of the Day
Your Stats teacher tells you your test score was the 3rd quartile for the class. Which is true?
I. You got 75% on the test.
II. You can’t really tell what this means without knowing the standard deviation.
III. You can’t really tell what this means unless the class distribution is nearly Normal.
A) none of these B) I only C) II only D) III only E) II and III
Chapter 6 The Standard Deviation as a Ruler and the Normal Model
Standard Deviation:
Using Standard Deviation as a Ruler
­is a measure of how far values are away from the mean
­we can use it to compare an individual value to the group by thinking about how many standard deviations it is "away" from the mean
Find the z­score for the following.
A mean of 45 with standard deviation 6.8
y = 53
y = 29
You get to drop the lowest(curved) score in your AP Euro class(I wish Mr. Stalter would do something like that, he sucks). Your Test 1 was a 90 and Test 2 was an 80. If the mean on Test 1 was 88 with a standard deviation of 4 and the mean on the second was 75 with a standard deviation of 5, which test did you do comparatively better on?
Changing Means(does that mean spread changes)
Construct a box plot for the following weights of men aged 19­24.
160
168
175
192
185
171
182
184
190
197
223
205
175
168
184
181
Suppose the average weight should be 170. How do we measure if someone is over/under weight? How "much" over/under weight? Does the distribution change when we change our graph to display how over/under weight each male is? What about changing units? When adding/subtracting constants ..................
When multiplying/dividing by a constant..............
With respect to z­scores
­shape is unaffected
­mean becomes 0
­makes the spread(standard deviation) 1
Standard Normal Model
Mean = 0
Standard Deviation = 1
When can you use the normal model?(if not told, you need to check)
­data is roughly symmetric
­is unimodal
The 68 ­95 ­ 99.7 Rule
The 68 ­95 ­ 99.7 Rule
Construct a normal model using the 68­95­99.7 Rule for birth weights of babies, N(7.6 lb, 1.3 lb)
Construct a normal model using the 68­95­99.7 Rule for ACT scores at a certain college, N(21.2, 4.4)
What percent of students scored between a 25.6 and a 30?
What percent of students scored between a 16.8 and 34.4? For ACT scores, the mean is 20.8 with a standard deviation of 4.8. Suppose your score is a 26(just over 1 standard deviation from the mean). Out of the senior class of 345 and assuming scores are normally distributed, how many seniors scored the same or lower than you?
For ACT scores, the mean is 20.8 with a standard deviation of 4.8. In the same class of 345 seniors, how many should score above a 35 or higher?
Using a z­score table
Find the percentage of students who scored lower than a 23 on the ACT.
(Assuming it is normal with a mean of 20.8 and standard deviation of 4.8, N(20.8,4.8))
Using a z­score table
Assuming it is normal with a mean of 20.8 and standard deviation of 4.8, N(20.8,4.8), find the percentage of students who scored lower than a 18 on the ACT. Find the percentage of students who scored higher than a 28.
Using a z­score table
Assuming it is normal with N(7.6 lb, 1.3 lb), find the percentage of births lower than a 4 lbs. Find the percentage of births higher than 10 lbs.
You got a 29 on your ACT. The mean is 20.8 with a standard deviation of 4.8. Harvard looks at SAT scores which have a mean of 1000 with a standard deviation of 250. Your equivalent ACT score needs to be above the 85%(a 1260 on the SAT). Do you qualify? Why or why not?
From Percentiles to Scores
Given the ACT scores with N(20.8,4.8) what score corresponds to the 25th percentile? 90th percentile?
From Percentiles to Scores
Given the ACT scores with N(20.8,4.8) what score corresponds to the highest 5%?
Normal Probability Plots
Create a data set that represents rolling 2 dice
(create a simulation using the calculator). You need 30 rolls(per group). Enter your data in a spreadsheet. Create a function(you will probably need the mean and standard deviation) to populate the next column with the corresponding z­score.
What does the "general" normal probability plot look like?
A concerned cizen who lives in a 20 mph zone recorded the speeds of 100 drivers going past his house. He found a normal distribuon with a mean of 23.84 mph and a standard deviaon of 3.56 mph. What percent of drivers were under the speed limit? Is it more unusual for a car to be going 10 mph or 34 mph? Why? Convert the mph to km(mulply by 1.609). What is the new mean and standard deviaon?
Suppose local law enforcement has an unwrien rule to give ckets to people speeding through a 20mph zone if they are going 28 mph or above. What percent of people are geng a cket?
IQ scores are approximately normal with a mean of 100 and standard deviaon of 16. Draw the model for IQ scores, making sure to label your 68‐95‐99.7 intervals.
What percent of people have IQ scores above 132?
What percent of people have IQ scores below 152?
MENSA(a nerdy organizaon for geniuses) allows membership to people in the 99th percenle. What is the lowest IQ score they allow?
What score corresponds to the 30th percenle?
Given Male weights with N(170 lbs, 19.8 lbs), find the following.
What weight corresponds to the 25th percenle?
What weight corresponds to the 90th percenle?
What percent of males are overweight(weight over 230lbs)?
In a normally distributed sample of 250 males, how many will weigh less than 150 lbs?
A company sells furniture that it claims can be assembled in “under an hour”. However, a large survey of customers found that only 25% of people could assemble it in 1 hour. The mean me for assembly was 1.29 hours. Assume the company feels mes are normally distributed.
Find the me corresponding to the 75
th
percenle and the IQR.
Find the standard deviaon.
What percent of people take more than 2 hours to assemble the furniture?
Chapter 6
Readings and examples: pgs 105 ­ 128
Homework: pgs 129­131:3­17,21,23,25,33,37,39,47
a
Chapters 2­6 Review assignment
pgs 135­142:2,3,6,10,19,25,26,32
Due by Tuesday at the beginning of class worth 4 pts Extra Credit on test
Exit slip
Mean weight for 19 year old males in the U.S. are around 172 lbs with a standard deviation of 11 lbs.
Mean weight for 19 year old females in the U.S. are around 148 lbs with a standard deviation of 12 lbs.
Is it more unusual for a male to weigh 250 lbs or a female to weigh 100 lbs?