Question

I mostly need questions 4-9, thank you!
NOTE: For question 1, you will be using the data file your instructor has provided you.

Coin
7
6
4
6
4
6
4
6
4
4
3
5
5
6
3
3
5
6
3
7
5
2
6
6
6
3
3
7
2
4
6
5
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7

1. (12 pts) Using the data file from your instructor, calculate descriptive statistics for the variable (Coin) where each of the thirty-five students in the sample flipped a coin 10 times. Round your answers to three decimal places and type the mean and the standard deviation in the grey area below.
   Mean:
   Standard deviation:

   NOTE: for questions 2-7, you will NOT be using the data file your instructor gave you. Please follow the instructions given in each question.

   3.(11 pts) List the probability value for each possibility in the binomial experiment calculated at the beginning of this lab, which was calculated with the probability of a success being ½. (Complete sentences not necessary; round your answers to three decimal places.)
   P(x=0)
   P(x=1)
   P(x=2)
   P(x=3)
   P(x=4)
   P(x=5)
   P(x=6)
   P(x=7)
   P(x=8)
   P(x=9)
   P(x=10)
   4. (12 pts) Give the probability for the following based on the calculations in question 3 above, with the probability of a success being ½. (Complete sentences not necessary; round your answers to three decimal places.)

2. P(x≥1)
   P(x>1)
   P(3<x ≤7)
   P(x<0)
   P(x≤3)
   P(x<3 or x≥7)
   5. Calculate (by hand) the mean and standard deviation for the binomial distribution with the probability of a success being ½ and n = 10. Either show your work or explain how your answer was calculated. Use these formulas to do the hand calculations: Mean = np, Standard Deviation =
   Mean =
   Standard Deviation =
   6. (7 pts) Calculate (by hand) the mean and standard deviation for the binomial distribution with the probability of a success being ¼ and n = 10. Write a comparison of these statistics to those from question 5 in a short paragraph of several complete sentences. Use these formulas to do the hand calculations: Mean = np, Standard Deviation =
   Mean =
   Standard Deviation =
   Comparison:
   7. Calculate (by hand) the mean and standard deviation for the binomial distribution with the probability of a success being ¾ and n = 10. Write a comparison of these statistics to those from question 6 in a short paragraph of several complete sentences. Use these formulas to do the hand calculations: Mean = np, Standard Deviation =
   Mean =
   Standard Deviation =
   Comparison:
   8. Using all four of the properties of a Binomial experiment (see page 201 in the textbook) explain in a short paragraph of several complete sentences why the Coin variable from the class survey represents a binomial distribution from a binomial experiment.
   9.(7 pts) Compare the mean and standard deviation for the Coin variable (question 1) with those of the mean and standard deviation for the binomial distribution that was calculated by hand in question 5. Explain how they are related in a short paragraph of several complete sentences.

   Mean from question #1:                       

   Standard deviation from question #1:   

   Mean from question #5:                         

   Standard deviation from question #5:    

   Comparison and explanation:

Answer 1

3)

Sample size , n =    10
Probability of an event of interest, p =   0.5

Binomial probability is given by

P(X=x) = C(n,x)*px*(1-p)(n-x)

X	P(X)
0	0.001
1	0.010
2	0.044
3	0.117
4	0.205
5	0.246
6	0.205
7	0.117
8	0.044
9	0.010
10	0.001

4)

P(x≥1)=0.9990

P(x>1)=0.989
P(3<x ≤7)=0.773
P(x<0)=0
P(x≤3)=0.172
P(x<3 or x≥7)=0.227

5)

Mean = np =    10*0.5=       5.000
Standard deviation = √(np(1-p)) =   √(10*0.5*(1-0.5))=       1.5811

6)

Mean = np =    10*0.25=       2.500
Standard deviation = √(np(1-p)) =   √(10*0.25*(1-0.25))=       1.3693

7)

Mean = np =    10*0.75=       7.500
Standard deviation = √(np(1-p)) =   √(10*0.75*(1-0.75))=       1.3693

8)

coin variable-

it is a binomial probability distribution,

because there is fixed number of trials,
only two outcomes are there, success and failure (head or tail)
trails are independent of each other

The probability of "success" p is the same for each outcome.