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 formula for calculating the standard deviation (s) of a probability distribution is:
s = √(Σ(x - μ)² * P(x))
Where x is the value (in this case, the number of cups of coffee), μ is the mean (1.471), and P(x) is the relative frequency of that value.
Using this formula with the given data, we get:
s = √((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)
s = √(2.595 + 0.324 + 0.122 + 0.052 + 0.039)
s = √3.132
s ≈ 1.772
Therefore, the answer is: 1.772.