Suppose W, X, and Y follow binomial distributions with the number of trials and probability of success as indicated below.W follows a binomial distribution with =nW4 trials and probability of success =pW0.1X follows a binomial distribution with =nX10 trials and probability of success =pX0.1Y follows a binomial distribution with =nY4 trials and probability of success =pY0.25(If necessary, consult a list of formulas.)(a)Find μW, μX, and μY, the respective means of W, X, and Y.=μW=μX=μY(b)The histograms of three binomial distributions are shown below. Match each of W, X, and Y with the histogram of its distribution.Histogram 10.050.100.150.200.250.300.350.400.450.500.550.600.650.700.75123456789100-1Distribution: ▼(Choose one)Histogram 20.050.100.150.200.250.300.350.400.450.500.550.600.650.700.75123456789100-1Distribution: ▼(Choose one)Histogram 30.050.100.150.200.250.300.350.400.450.500.550.600.650.700.75123456789100-1Distribution: ▼(Choose one)CheckSave For LaterSubmit AssignmentTerms of Use|Privacy Center|Accessibility
Question
Suppose W, X, and Y follow binomial distributions with the number of trials and probability of success as indicated below.W follows a binomial distribution with =nW4 trials and probability of success =pW0.1X follows a binomial distribution with =nX10 trials and probability of success =pX0.1Y follows a binomial distribution with =nY4 trials and probability of success =pY0.25(If necessary, consult a list of formulas.)(a)Find μW, μX, and μY, the respective means of W, X, and Y.=μW=μX=μY(b)The histograms of three binomial distributions are shown below. Match each of W, X, and Y with the histogram of its distribution.Histogram 10.050.100.150.200.250.300.350.400.450.500.550.600.650.700.75123456789100-1Distribution: ▼(Choose one)Histogram 20.050.100.150.200.250.300.350.400.450.500.550.600.650.700.75123456789100-1Distribution: ▼(Choose one)Histogram 30.050.100.150.200.250.300.350.400.450.500.550.600.650.700.75123456789100-1Distribution: ▼(Choose one)CheckSave For LaterSubmit AssignmentTerms of Use|Privacy Center|Accessibility
Solution
The mean of a binomial distribution is calculated by multiplying the number of trials (n) by the probability of success (p).
(a) For W, μW = nW * pW = 4 * 0.1 = 0.4 For X, μX = nX * pX = 10 * 0.1 = 1 For Y, μY = nY * pY = 4 * 0.25 = 1
(b) Without the histograms, it's impossible to match each of W, X, and Y with the histogram of its distribution. However, you would typically match them based on the mean of each distribution. The distribution with the lowest mean would match with the histogram that has the most weight towards the lower numbers, and vice versa.
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