# use this coin 5 4 3 2 4 4 5 4 3 4 7 2 3 3 5 5 4 3 7 2 7 2 2 3 5 4 2 5 2 2 4 7 2 6 4 this coin is for number 2 question Statistical Concepts:

P(4<x ≤7)

P(x<4 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 work or explain how your answer was calculated. Use these formulas to do the hand calculations: Mean = np, Standard Deviation =          (4 points)

Mean = np:

Standard Deviation = :

6.     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.  (4 points)

In order to explain the meaning and utility of distributions, it is necessary to first introduce the topic of random variables. The term random in Random Variable refers to the idea that each individual outcome has an equal chance of occurring. Therefore, each outcome is random determined. For example, a fair coin has an equal probability of flipping up heads as it does flipping up tails. Hance, the random variable is determined by the outcome of flipping a coin.

7.     Compare the mean and standard deviation for the Coin variable (question 2) 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.    (4 points)

Mean from question #2

Standard deviation:

Mean from question #5

Standard deviation from question #5:

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