Answer to Question #252572 in Statistics and Probability for rasha

Question

The number of days required for two suppliers to deliver orders is as follows. Supplier A: 11 10 9 10 11 11 10 11 10 10 Supplier B: 8 10 13 7 10 11 10 7 15 12 Where, the average number of days required for supplier A to deliver orders = 1.47 weeks and Standard Deviation = 0.10 week | P a g e 2 1) Which supplier provides more consistent and homogenous delivery times A or B? Justify your answer. 2) Without any calculation, and if the unit of measurement changes to be in hours, will the homogeneity be the same? 3) And do you think the delivery time for each supplier is symmetric. Support your answer with a proper test for skewness. 4) Prove that ∑ (𝑋𝑖 − 𝑋̅) = 0 𝑛 𝑖=1 Q

Answer 1

1)

for supplier B:

mean:

$\mu_B=\frac{\sum x)i}{n}=10.3$

Standard Deviation:

$\sigma_B=\sqrt{\frac{\sum (x_-\mu_B)^2}{n}}=2.45$

Since $\sigma_A<\sigma_B$ , supplier A provides more consistent and homogenous delivery times.

2)

the homogeneity will be changed, since new standard deviation will be increased:

$\sigma'_A=24\sigma_A$

$\sigma'_B=24\sigma_B$

3)

SKEWNESS = $\frac{\frac{1}{n}\sum(x_i-\mu)^3}{(\frac{1}{n}\sum(x_i-\mu)^2)^{3/2}}$

SKEWNESS_A = -0.43

Since -0.5 < SKEWNESS_A < 0.5, delivery time for supplier A is approximately symmetric.

SKEWNESS_B = 0.36

Since -0.5 < SKEWNESS_B < 0.5, delivery time for supplier B is approximately symmetric.

4)

$\sum (x_i-\overline{x})=x_1-\overline{x}+x_2-\overline{x}+x_3-\overline{x}+...+x_n-\overline{x}=$

$=\sum x_i-n\overline{x}=\sum x_i-\sum x_i=0$