Question

refer to the accompanying table, which describes the number of adults in groups of five. find the mean and standard deviation for the numbers of sleepwalkers in groups of five.
click the icon to view the data table.
the mean is
sleepwalker(s). (round to one decimal place as needed.)
table of numbers of sleepwalkers and probabilities
print
done

Explanation:

Step1: Recall the formula for the mean of a discrete probability distribution

The formula for the mean \(\mu\) of a discrete probability distribution is \(\mu=\sum_{x}x\cdot P(x)\)

Step2: Calculate each \(x\cdot P(x)\) term

• For \(x = 0\): \(0\times0.173=0\)
• For \(x = 1\): \(1\times0.355 = 1.355\)
• For \(x = 2\): \(2\times0.308=0.616\)
• For \(x = 3\): \(3\times0.135 = 0.405\)
• For \(x = 4\): \(4\times0.025=0.1\)
• For \(x = 5\): \(5\times0.004 = 0.02\)

Step3: Sum up the \(x\cdot P(x)\) terms

\(\mu=0 + 1.355+0.616 + 0.405+0.1+0.02\)
\(\mu=1.496\approx1.5\)

Answer:

\(1.5\)