Answer:
a) mean = 20.75
b) variance = 1.6274
c) standard deviation = 1.2757
d) 145 arrangements per week.
Step-by-step explanation:
We have the following distribution:
x 19 20 21 22 23
P(x) 0.21 0.22 0.30 0.15 0.12
Mean: Is the average of the data. To find the mean, you need to take every x and multiply it by its corresponding P(x) and sum these values. The result will be the mean.
μ =∑ (x·P(x))
Therefore, in this case we have:
μ = 19(0.21) + 20(0.22) + 21(0.30) + 22(0.15) + 23 (0.12) = 20.75
Thus, the mean is 20.75
Variance: To calculate the variance you need to subtract the mean to every value x, then square the result and multiply it by the probability. Finally, you sum up these results and you get the variance.
In this case we will have
19 - 20.75 = -1.75 ⇒ (-1.75)²(0.21) =<u> 0.6431</u>
20 - 20.75 = -.75 ⇒(0.75)²(0.22) = <u>0.1237</u>
21 - 20.75 = 0.25 ⇒(0.25)²(0.30) = <u>0.0187</u>
22 - 20.75 = 1.25 ⇒(1.25)²(0.15) = <u>0.2344</u>
23 - 20.75 = 2.25 ⇒ (2.25)²(0.12) = <u>0.6075</u>
Now we need to sum up these results:
0.6431 + 0.1237 + 0.0187 + 0.2344 + 0.6075 = 1.6274
The variance is 1.6274.
Standard Deviation: It is the root of the variance.
Therefore, the standard deviation will be √1.6274 = 1.2757
b) How many arrangements should the florist expect to deliver each week, rounded to the nearest whole number?
To answer this question we'll work with the mean, he expects to deliver 20.75 arrangements per day, therefore, per week he'd deliver:
20.75 (7) = 145.25 = 145 arrangements.
