More Binomial Practice-1

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Feb 20, 2024

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More Binomial Practice 1. A d8 dice is rolled 20 times. If a roll ends up as a 7 or 8, it is considered a success. n= 20 p= .25 a. Why does this meet all the requirements to be binomial? There is a success or failure. There is a fixed number of trials. - 20 trials - independent b. Find the mean and standard deviation of the number of successes expected. Mean = n*p = 5 Stand dev= 1.94 c. Find the probability of exactly 6 of those rolls being a success. .1686 d. Find the probability of less than 6 of those rolls being a success. Binomcdf(20, .25, 5) .6171 e. Find the probability of at most 6 of those rolls being a success. Binomcdf(20, .25, 6) .7858 f. Find the probability of more than 6 of those rolls being a success. 1-binomcdf(20, .25, 6)

=0.2142 2. A study of M&Ms color distributions is done (that is a thing), and green M&Ms are found to make up 16% of all the different colors. Assume a random sample of 100 M&Ms is obtained and answer the questions below. N= 100 p= .16 a. Why does this meet all the requirements to be binomial? b. Find the mean and standard deviation of the number of green M&Ms expected. (Round to the nearest M&M) mean= 16 stand dvt= 3.67 c. What would be the cutoff values for significantly high and significantly low observations of green M&Ms in this random sample? 16- 2(4) =100 24= high d. Find the probability of getting 26 or more green M&Ms. Is that probability unusual? Compare it to the interval from part c. Do they agree with each other? .0071

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