Find the mean for the data. The data represents the costs of nine compact refrigerators rated very good or excellent by Consumer Reports on their website.

What is the difference between the mean, median, and mode?

What are the mean and standard deviation of a binomial probability distribution with n=17 and ${\displaystyle p=\frac{18}{32}}$?

a) Explain whether the situation involves comparing proportions for two groups or comparing two proportions from the same group.
Also, check whether the methods of the section apply to the difference in proportions.
b) Explain whether the situation involves comparing proportions for two groups or comparing two proportions from the same group. Also, check whether the methods of the section apply to the difference in proportions.
c) Explain whether the situation involves comparing proportions for two groups or comparing two proportions from the same group. Also, check whether the methods of the section apply to the difference in proportions.
d) Explain whether the situation involves comparing proportions for two groups or comparing two proportions from the same group. Also, check whether the methods of the section apply to the difference in proportions.

The lengths of the products produced in a production process are controlled. The standard deviation is 0.45 mm. A quality control specialist keeps checking over 40 units randomly every morning. Average length in one day 35.62mm. when it happens; Which of the following is the confidence interval for the mean population mean at ${\displaystyle 95\mathrm{\%}}$ confidence level?
A) ${\displaystyle P\left(60<\mu <70\right)=0,95}$
B) ${\displaystyle P\left(30<\mu <40\right)=0,05}$
C) ${\displaystyle P\left(30<\mu <40\right)=0,95}$
D) ${\displaystyle P\left(60<\mu <70\right)=0,05}$
E) ${\displaystyle P\left(70<\mu <80\right)=0,95}$

Let ${\displaystyle X_1\dots .,X_n\text{and}{Y}_1,\dots ,Y_m}$ be two sets of random variables. Let ${\displaystyle a_i,b_j}$ be arbitrary constant.
Show that
${\displaystyle Cov(\sum _{i=1}^n{a}_i{X}_i,\sum _{j=1}^m{b}_j{Y}_j)=\sum _{i=1}^n\sum _{j=1}^m{a}_i{b}_{j}Cov(X_i,Y_j)}$

The random variables X and Y have joint density function
f(x,y)=12xy(1-x) 0<x<1,0<y<1
and equal to 0 otherwise.
Find Var(Y).

750 units of product are produced in 3 different production lines. It is desired to investigate whether there is a difference between the production lines at the 95% confidence level. Find the chi-square calculation value.
a. 514
b. 20
c. 45
d. 34
$\begin{array}{|ccc|}\hline \text{ Production line }& \text{ Observed }& \text{ Expected }\\ \text{ A }& 250& 250\\ \text{ B }& 200& 250\\ \text{ C }& {300}^{2}50\\ \text{ Total }& 750& 750\\ \hline\end{array}$