A fair coin is flipped 104 times. Let x be the number of heads. What normal distributions best approximates x?

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.

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

Statistics from Cornell's Northeast Regional Climate Center indicate that Ithaca, New York, gets an average of 35.4" of rain each year, with a standard deviation of 4.2". Assume that a Normal model applies. a) During what percentage of years does Ithaca get more than 40" of rain? b. Less than how much rain falls in the driest 20% of all years? c. A Cornell University student is in Ithaca for 4 years. Let ${\displaystyle \bar{y}}$ represent the mean amount of rain for those 4 years. Describe the sampling distribution model of this sample mean, ${\displaystyle \bar{y}}$. d) What 's the probability that those 4 years average less than 30" of rain?

Answer true or false to each statement. Explain your answers.
a. Two normal distributions that have the same mean are centered at the same place, regardless of the relationship between their standard deviations.
b. Two normal distributions that have the same standard deviation have the same spread, regardless of the relationship between their means.

Each child has probability 25% of having blood type O. We have 22 children and we want to find the odds that exactly 2 of them have type O blood. Find the expected value.

Which would you expect to have a density curve that is higher at the mean: the standard normal distribution or a normal distribution with standard deviation 0.5? Explain.