The student will compare and contrast empirical data from a random number generator with the uniform distribution.
Collect the data
Use a random number generator to generate 50 values between zero and one (inclusive). List them in
[link] . Round the numbers to four decimal places or set the calculator MODE to four places.
Complete the table.
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Calculate the following:
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s = _______
first quartile = _______
third quartile = _______
median = _______
Organize the data
Construct a histogram of the empirical data. Make eight bars.
Construct a histogram of the empirical data. Make five bars.
Describe the data
In two to three complete sentences, describe the shape of each graph. (Keep it simple. Does the graph go straight across, does it have a V shape, does it have a hump in the middle or at either end, and so on. One way to help you determine a shape is to draw a smooth curve roughly through the top of the bars.)
Describe how changing the number of bars might change the shape.
Theoretical distribution
In words,
X = _____________________________________.
The theoretical distribution of
X is
X ~
U (0,1).
In theory, based upon the distribution
X ~
U (0,1), complete the following.
μ = ______
σ = ______
first quartile = ______
third quartile = ______
median = __________
Are the empirical values (the data) in the section titled
Collect the Data close to the corresponding theoretical values? Why or why not?
Plot the data
Construct a box plot of the data. Be sure to use a ruler to scale accurately and draw straight edges.
Do you notice any potential outliers? If so, which values are they? Either way, justify your answer numerically. (Recall that any DATA that are less than
Q1 – 1.5(
IQR ) or more than
Q3 + 1.5(
IQR ) are potential outliers.
IQR means interquartile range.)
Compare the data
For each of the following parts, use a complete sentence to comment on how the value obtained from the data compares to the theoretical value you expected from the distribution in the section titled
Theoretical Distribution .
minimum value: _______
first quartile: _______
median: _______
third quartile: _______
maximum value: _______
width of
IQR : _______
overall shape: _______
Based on your comments in the section titled
Collect the Data , how does the box plot fit or not fit what you would expect of the distribution in the section titled
Theoretical Distribution ?
Discussion question
Suppose that the number of values generated was 500, not 50. How would that affect what you would expect the empirical data to be and the shape of its graph to look like?
Wayne and Dennis like to ride the bike path from Riverside Park to the beach. Dennis’s speed is seven miles per hour faster than Wayne’s speed, so it takes Wayne 2 hours to ride to the beach while it takes Dennis 1.5 hours for the ride. Find the speed of both bikers.
from theory: distance [miles] = speed [mph] × time [hours]
info #1
speed_Dennis × 1.5 = speed_Wayne × 2
=> speed_Wayne = 0.75 × speed_Dennis (i)
info #2
speed_Dennis = speed_Wayne + 7 [mph] (ii)
use (i) in (ii) => [...]
speed_Dennis = 28 mph
speed_Wayne = 21 mph
George
Let W be Wayne's speed in miles per hour and D be Dennis's speed in miles per hour. We know that W + 7 = D and W * 2 = D * 1.5.
Substituting the first equation into the second:
W * 2 = (W + 7) * 1.5
W * 2 = W * 1.5 + 7 * 1.5
0.5 * W = 7 * 1.5
W = 7 * 3 or 21
W is 21
D = W + 7
D = 21 + 7
D = 28
Salma
Devon is 32 32 years older than his son, Milan. The sum of both their ages is 54 54. Using the variables d d and m m to represent the ages of Devon and Milan, respectively, write a system of equations to describe this situation. Enter the equations below, separated by a comma.
please why is it that the 0is in the place of ten thousand
Grace
Send the example to me here and let me see
Stephen
A meditation garden is in the shape of a right triangle, with one leg 7 feet. The length of the hypotenuse is one more than the length of one of the other legs. Find the lengths of the hypotenuse and the other leg
however, may I ask you some questions about Algarba?
Amoon
hi
Enock
what the last part of the problem mean?
Roger
The Jones family took a 15 mile canoe ride down the Indian River in three hours. After lunch, the return trip back up the river took five hours. Find the rate, in mph, of the canoe in still water and the rate of the current.
Shakir works at a computer store. His weekly pay will be either a fixed amount, $925, or $500 plus 12% of his total sales. How much should his total sales be for his variable pay option to exceed the fixed amount of $925.
I'm guessing, but it's somewhere around $4335.00 I think
Lewis
12% of sales will need to exceed 925 - 500, or 425 to exceed fixed amount option. What amount of sales does that equal? 425 ÷ (12÷100) = 3541.67. So the answer is sales greater than 3541.67.
Check:
Sales = 3542
Commission 12%=425.04
Pay = 500 + 425.04 = 925.04.
925.04 > 925.00
Munster
difference between rational and irrational numbers
Jazmine trained for 3 hours on Saturday. She ran 8 miles and then biked 24 miles. Her biking speed is 4 mph faster than her running speed. What is her running speed?