Suppose X follows a binomial distribution with =n30 trials and probability of success =p0.50.(If necessary, consult a list of formulas.)(a)Find μX, the mean of X. Do not round your answer.=μX(b)The histograms of three binomial distributions are shown below. Choose the one that could be the histogram of the distribution of X.Histogram A0.050.100.150.20510152025300-1Histogram B0.050.100.150.20510152025300-1Histogram C0.050.100.150.20510152025300-1CheckSave For LaterSubmit AssignmentTerms of Use|Privacy Center|Accessibility
Question
Suppose X follows a binomial distribution with =n30 trials and probability of success =p0.50.(If necessary, consult a list of formulas.)(a)Find μX, the mean of X. Do not round your answer.=μX(b)The histograms of three binomial distributions are shown below. Choose the one that could be the histogram of the distribution of X.Histogram A0.050.100.150.20510152025300-1Histogram B0.050.100.150.20510152025300-1Histogram C0.050.100.150.20510152025300-1CheckSave For LaterSubmit AssignmentTerms of Use|Privacy Center|Accessibility
Solution
(a) The mean (μX) of a binomial distribution is calculated by the formula μX = n*p. Here, n is the number of trials and p is the probability of success. Given n=30 and p=0.50, we can substitute these values into the formula:
μX = np μX = 300.50 μX = 15
So, the mean of X is 15.
(b) Without the visual representation of the histograms, it's impossible to determine which one could be the histogram of the distribution of X. However, for a binomial distribution with n=30 and p=0.50, the histogram should be symmetric around the mean (which is 15 in this case). So, the correct histogram would be the one that is symmetric around 15.
Similar Questions
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