The student will compare empirical data and a theoretical distribution to determine if an everyday experiment fits a discrete distribution.
The student will demonstrate an understanding of long-term probabilities.
Supplies
One full deck of playing cards
Procedure
The experimental procedure is to pick one card from a deck of shuffled cards.
The theoretical probability of picking a diamond from a deck is _________.
Shuffle a deck of cards.
Pick one card from it.
Record whether it was a diamond or not a diamond.
Put the card back and reshuffle.
Do this a total of ten times.
Record the number of diamonds picked.
Let
X = number of diamonds. Theoretically,
X ~
B (_____,_____)
Organize the data
Record the number of diamonds picked for your class in
[link] . Then calculate the relative frequency.
x
Frequency
Relative Frequency
0
__________
__________
1
__________
__________
2
__________
__________
3
__________
__________
4
__________
__________
5
__________
__________
6
__________
__________
7
__________
__________
8
__________
__________
9
__________
__________
10
__________
__________
Calculate the following:
= ________
s = ________
Construct a histogram of the empirical data.
Theoretical distribution
Build the theoretical PDF chart based on the distribution in the
Procedure section.
x
P (
x )
0
1
2
3
4
5
6
7
8
9
10
Calculate the following:
μ = ____________
σ = ____________
Construct a histogram of the theoretical distribution.
Using the data
Note
RF = relative frequency
Use the table from the
Theoretical Distribution section to calculate the following answers. Round your answers to four decimal places.
P (
x = 3) = _______________________
P (1<
x <4) = _______________________
P (
x ≥ 8) = _______________________
Use the data from the
Organize the Data section to calculate the following answers. Round your answers to four decimal places.
RF (
x = 3) = _______________________
RF (1<
x <4) = _______________________
RF (
x ≥ 8) = _______________________
Discussion questions
For questions 1 and 2, think about the shapes of the two graphs, the probabilities, the relative frequencies, the means, and the standard deviations.
Knowing that data vary, describe three similarities between the graphs and distributions of the theoretical and empirical distributions. Use complete sentences.
Describe the three most significant differences between the graphs or distributions of the theoretical and empirical distributions.
Using your answers from questions 1 and 2, does it appear that the data fit the theoretical distribution? In complete sentences, explain why or why not.
Suppose that the experiment had been repeated 500 times. Would you expect
[link] or
[link] to change, and how would it change? Why? Why wouldn’t the other table change?
Step 1: Find the mean. To find the mean, add up all the scores, then divide them by the number of scores. ...
Step 2: Find each score's deviation from the mean. ...
Step 3: Square each deviation from the mean. ...
Step 4: Find the sum of squares. ...
Step 5: Divide the sum of squares by n – 1 or N.
The sample of 16 students is taken. The average age in the sample was 22 years with astandard deviation of 6 years. Construct a 95% confidence interval for the age of the population.
Bhartdarshan' is an internet-based travel agency wherein customer can see videos of the cities they plant to visit. The number of hits daily is a normally distributed random variable with a mean of 10,000 and a standard deviation of 2,400
a. what is the probability of getting more than 12,000 hits?
b. what is the probability of getting fewer than 9,000 hits?
Bhartdarshan'is an internet-based travel agency wherein customer can see videos of the cities they plan to visit. The number of hits daily is a normally distributed random variable with a mean of 10,000 and a standard deviation of 2,400.
a. What is the probability of getting more than 12,000 hits