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Practice with the Normal Model & Describing Distributions
Practice with the Normal Model
& Describing Distributions
First up: the Normal Model
Suppose a University of Texas professor wanted to study the distance a squirrel travels from their nest to search for food. He randomly selects 50 squirrels to study.
Each selected squirrel is captured and a locating device is placed on the squirrel’s ankle. Then each squirrel is returned to campus and monitored for one month.
Don’t worry - there will not be any dying squirrels in this lesson….
The professor finds that the distance squirrels travel for food each day is normally distributed, with a mean of 100 feet, and a standard deviation of 10 feet.
What proportion of squirrels travel less than 78 feet?
...but if you’ve ever been assaulted by a campus squirrel, you might wish...
The professor finds that the distance squirrels travel for food each day is normally distributed, with a mean of 100 feet, and a standard deviation of 10 feet.
What proportion of squirrels travel less than 78 feet?
...but if you’ve ever been assaulted by a campus squirrel, you might wish...
0.0139
What proportion of randomly selected squirrels would travel more than 115 feet for food in a day?
Campus squirrels: The sole purpose of our existence is to feed them - or so they think.
What proportion of randomly selected squirrels would travel more than 115 feet for food in a day?
Campus squirrels: The sole purpose of our existence is to feed them - or so they think.
0.0668
What proportion of randomly selected squirrels travel between 80 and 90 feet from their nests for food?
Look at this little bugger - he’s just waiting to jump out of nowhere and pilfer your sandwich.
What proportion of randomly selected squirrels travel between 80 and 90 feet from their nests for food?
Look at this little bugger - he’s just waiting to jump out of nowhere and pilfer your sandwich.
0.2857
What would be the cut off for the furthest 10% of the distances squirrels travel for food each day?
No, small child! Do not feed the squirrels! You’re just empowering them!!
What would be the cut off for the furthest 10% of the distances squirrels travel for food each day?
No, small child! Do not feed the squirrels! You’re just empowering them!!
112.816 feet
Practice with Describing Distributions
1. Based on the 5-number summary, what appears to be the shape of the distribution?
a) Skewed to the leftb) Skewed to the rightc) Unimodal and roughly symmetricd) Roughly symmetrice) Bimodal
Min Q1 Median Q3 Max50 65 75 85 100
1. Based on the 5-number summary, what appears to be the shape of the distribution?
a) Skewed to the leftb) Skewed to the rightc) Unimodal and roughly symmetricd) Roughly symmetrice) Bimodal
Min Q1 Median Q3 Max50 65 75 85 100
2. Based on the 5-number summary, what appears to be the shape of the distribution?
a) Skewed to the leftb) Skewed to the rightc) Unimodal and roughly symmetricd) Roughly symmetrice) Multimodal
Min Q1 Median Q3 Max64 81 91 93 99
2. Based on the 5-number summary, what appears to be the shape of the distribution?
a) Skewed to the leftb) Skewed to the rightc) Unimodal and roughly symmetricd) Roughly symmetrice) Multimodal
Min Q1 Median Q3 Max64 81 91 93 99
3. Based on the 5-number summary, what appears to be the shape of the distribution?
a) Skewed to the leftb) Skewed to the rightc) Unimodal and roughly symmetricd) Roughly symmetrice) Multimodal
Min Q1 Median Q3 Max28 34 39 55 83
3. Based on the 5-number summary, what appears to be the shape of the distribution?
a) Skewed to the leftb) Skewed to the rightc) Unimodal and roughly symmetricd) Roughly symmetrice) Multimodal
Min Q1 Median Q3 Max28 34 39 55 83
4. In which direction is this distribution LIKELY skewed?
a) Skewed to the leftb) Skewed to the right
Mean Median80 74
4. In which direction is this distribution LIKELY skewed?
a) Skewed to the leftb) Skewed to the right
Mean Median80 74
5. In which direction is this distribution LIKELY skewed?
a) Skewed to the leftb) Skewed to the right
Mean Median17.2 22.5
5. In which direction is this distribution LIKELY skewed?
a) Skewed to the leftb) Skewed to the right
Mean Median17.2 22.5
6. Which of the following is a reasonable estimate of the STANDARD DEVIATION of this distribution?
a) 10b) 30c) 100d) 200e) 480
6. Which of the following is a reasonable estimate of the STANDARD DEVIATION of this distribution?
a) 10b) 30c) 100d) 200e) 480
7. Which of the following is a reasonable estimate of the STANDARD DEVIATION of this distribution?
a) 10b) 30c) 100d) 200e) 480
7. Which of the following is a reasonable estimate of the STANDARD DEVIATION of this distribution?
a) 10b) 30c) 100d) 200e) 480
8. You are given the mean, standard deviation, and max value of a distribution. Would the normal model be appropriate for this distribution? Explain.
Mean St. Dev. Max
89 8.4 95
8. You are given the mean, standard deviation, and max value of a distribution. Would the normal model be appropriate for this distribution? Explain.
Mean St. Dev. Max
89 8.4 95In a normal distribution, we expect the max value to be at least 2 standard deviations above the mean. In this case, the max is less than one standard deviation above the mean, which suggest that the distribution is skewed to the left (lower numbers). The Normal Model would NOT be appropriate for this distribution.
Percent of golfers by age
Cumulative Frequency Distributions...
Roughly 28% of golfers are age 39
or younger
Percent of golfers by age
Cumulative Frequency Distributions...
Roughly 60% of golfers are age 59
or younger
Percent of golfers by age
Cumulative Frequency Distributions...
What is the median age for golfers?
About 50 years
old
