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 =pW0.8X follows a binomial distribution with =nX8 trials and probability of success =pX0.4Y follows a binomial distribution with =nY8 trials and probability of success =pY0.8(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 10.050.100.150.200.250.300.350.400.450.500.55123456789100-1Distribution: ▼(Choose one)Histogram 20.050.100.150.200.250.300.350.400.450.500.55123456789100-1Distribution: ▼(Choose one)Histogram 30.050.100.150.200.250.300.350.400.450.500.55123456789100-1Distribution: ▼(Choose one)
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 =pW0.8X follows a binomial distribution with =nX8 trials and probability of success =pX0.4Y follows a binomial distribution with =nY8 trials and probability of success =pY0.8(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 10.050.100.150.200.250.300.350.400.450.500.55123456789100-1Distribution: ▼(Choose one)Histogram 20.050.100.150.200.250.300.350.400.450.500.55123456789100-1Distribution: ▼(Choose one)Histogram 30.050.100.150.200.250.300.350.400.450.500.55123456789100-1Distribution: ▼(Choose one)
Solution
(a) The mean of a binomial distribution is calculated by multiplying the number of trials by the probability of success.
For W, μW = nW * pW = 4 * 0.8 = 3.2
For X, μX = nX * pX = 8 * 0.4 = 3.2
For Y, μY = nY * pY = 8 * 0.8 = 6.4
(b) Without the actual histograms, it's impossible to match each of W, X, and Y with the histogram of its distribution. However, you would generally expect the distribution with the highest mean (Y in this case) to be skewed towards the right, and the distributions with lower means (W and X in this case) to be skewed towards the left.
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