Please answer question 6. Part 1 (2 points). Create a Binomial Probability Distribution for tossing a coin 10 times wh

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Please answer question 6.
Part 1 (2 points). Create aBinomial Probability Distribution for tossing a coin 10 times wheresuccess is “Heads”. Therefore, the total number oftrials n = 10 and the probability of success p =0.5. Round the probabilities to three decimalplaces. (You can use the GeoGebra app to find each ofthese.)
Fill in the Binomial Probability Distribution Table forP(x):
X
P(x)
0
0.01
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
You will be using this Binomial Probability Distribution toanswer some of the questions below.
Part 2 (2 points). Using thebinomial probability distribution that you just constructed,calculate the following probabilities. Round to threedecimal places.
P(x > 1) = __0.989_________
P(x < 4) = ___0.377________
P(4 < x < 7) = ____0.568______
Part 3 (1 point). Using the formulasfor mean and standard deviation that you learned in Chapter 4 forthe Binomial Distribution, calculate the mean and standarddeviation for this binomial probabilitydistribution. Round you answers to three decimalplaces.
Mean = ___5_______
Standard Deviation = ______1.581____
Part 4 (2 points). Using all of thecriteria of a Binomial Experiment shown in the boxesbelow, explain in a short paragraph of severalcomplete sentences why the Coin Tossing variable in Part 1represents a binomial probability experiment.
For instance, a binomial experiment has only two outcomes(success vs failure)… You want to identify theses outcomes for theCoin experiment and determine which outcome is considered a successand which is considered a failure. Then, you want to dothe same for all of the other criteria of a Binomial Experimentshown in the box below.
A binomial experiment is a probability experiment that satisfiesthese conditions:
The coin toss had a fixed number of trials that were independentof each other. There were 10 total trials. The possibleoutcomes were Heads or Tails (success or Failure). Theprobability of heads or tails is the same for each toss,0.5.
Notation for Binomial Experiments
Symbol
Description
n
The number of trials
p
The probability of success in a single trial
q
The probability of failure in a single trial (q = 1 – p)
x
The random variable represents a count of the number ofsuccesses in n trials: x = 0, 1, 2, 3, …, n.
Part 5 (2 points). Now, using thefollowing coin toss results from a sample survey of 35 differentstudents – showing how many heads were tossed out of 10 tosses,find the mean and standard deviation of thedata. Hint: Type all 35 data points intoGeoGebra. Then find the sample mean and standarddeviation (round to 3 decimal places).
5
4
7
5
7
4
4
4
5
2
4
2
2
7
3
4
3
3
2
5
2
2
3
3
7
3
2
6
4
4
5
2
5
2
4
Mean = _____3.886_____
Standard Deviation = __1.604________
Part 6 (1 point). Compare the meanand standard deviation that you calculated in Part 3 (from theformulas) to the mean and standard deviation that you calculated inPart 5.
Write a few complete sentences explaining how they compare toeach other. In other words, if these values aredifferent, why do you think they are different, etc.