Answer :
Answer:
A) Mean: 1000; Standard deviation: 100
Step-by-step explanation:
In four weeks the weekly outputs are
Week 1: 900
Week 2: 1100
Week 3: 900
Week 4: 1100
Total for 4 weeks: 900 + 1100 + 900 + 1100 = 4,000
Weekly mean = Total/number of weeks = 4000/4 = 1000
The variance from the mean, [tex]\sigma^2[/tex] is the sum of the squares of the deviations from the mean divided by the total number of observations
[tex]\sigma^2 = \dfrac{(900 - 1000)^2 + (1100-1000)^2 + (900-1000)^2 + (\\1100- 1000)^2}{4}\\= \dfrac{100^2 + 100^2 + 100^2 + 100^2}{4}\\= \dfrac{4 \cdot 100^2}{4}\\\\= 100^2\\\\[/tex]
The standard deviation from the mean, [tex]\sigma[/tex], is the square root of the variance
[tex]\sigma = \sqrt{100^2} = 100 \quad\text{since $\sqrt{x^2} =x$}[/tex]
Mean = 1000
Standard deviation = 100
