Alex tracked the number of cups of coffee he drank each day for the following month and created a new
probability distribution.
Number of Cups of Coffee, 0 1 2 3 4
Relative Frequency, 0.035 0.579 0.286 0.080 0.020
According this new data, Alex is expected to drink 1.471 cups per day
4. Calculate s(x) of Alexʼs new probability distribution. (1 point)
0.599
0.775
1.471
4.223
The s(x) of a probability distribution is the standard deviation, which measures the spread of the data around the mean. It can be calculated using the formula:
s(x) = √[Σ(xi - μ)²p(x)]
where xi is each data point, μ is the mean, and p(x) is the relative frequency.
Using the given data, we have:
μ = Σ(xi * p(x)) = 0(0.035) + 1(0.579) + 2(0.286) + 3(0.080) + 4(0.020) = 1.471
s(x) = √[Σ(xi - μ)²p(x)]
= √[(0-1.471)²(0.035) + (1-1.471)²(0.579) + (2-1.471)²(0.286) + (3-1.471)²(0.080) + (4-1.471)²(0.020)]
= √[0.363 + 0.392 + 0.186 + 0.246 + 0.186]
= √1.373
≈ 1.171
Therefore, the answer is not given in the options. The closest option is 0.775, but that is not correct.