Why do two normal distributions that have equal standard deviations have the same shape?

The manager of the store in the preceding exercise calculated the residual for each point in the scatterplot and made a dotplot of the residuals.
The distribution of residuals is roughly Normal with a mean of $0 and standard deviation of $22.92.
The middle 95% of residuals should be between which two values? Use this information to give an interval of plausible values for the weekly sales revenue if 5 linear feet are allocated to the stores

Describe in words the surface whose equation is given. (assume that r is not negative.) $\theta =\frac{\pi }{4}$
a) The plane $y=-z$ where y is not negative
b) The plane $y=z$ where y and z are not negative
c) The plane $y=x$ where x and y are not negative
d) The plane $y=-x$ where y is not negative
e) The plane $x=z$ where x and y are not negative

Explain why t distributions tend to be flatter and more spread out than the normal distribution.

Basic Computation:$\hat{p}$ Distribution Suppose we have a binomial experiment in which success is defined to be a particular quality or attribute that interests us.
(a) Suppose $n=33$ and $p=0.21$. Can we approximate the $\hat{p}$
distribution by a normal distribution? Why? What are the values of ${\mu }_{\hat{p}}$ and ${\sigma }_{\hat{p}}$.?

Find the expected count and the contribution to the chi-square statistic for the (Group 1, Yes) cell in the two-way table below.
$\begin{array}{|cccc|}\hline & \text{Yes}& \text{No}& \text{Total}\\ \text{Group 1}& 710& 277& 987\\ \text{Group 2}& 1175& 323& 1498\\ \text{Total}& 1885& 600& 2485\\ \hline\end{array}$
Round your answer for the excepted count to one decimal place, and your answer for the contribution to the chi-square statistic to three decimal places.
Expected count=?
contribution to the chi-square statistic=?

You randomly survey shoppers at a supermarket about whether they use reusable bags. Of 60 male shoppers 15 use reusable bags. Of 110 female shoppers, 60 use reusable bags. Organize your results in a two-way table. Include the marginal frequencies.

The following data represents the age of 30 lottery winners. 21 49 54 63 54 35 52 45 88 65 64 51 41 34 49 78 31 40 51 70 78 60 74 55 29 66 59 32 68 56 Complete the frequency distribution for the data. Bin Frequency 20-29 30-39 40-49 50-59 60-69 70-79 80-89