# Final Exam

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Contents

## Question 1

Is the relationship expressed by this scatter plot linear and is it exact? Please check all that apply.

## Question 2

For this data, tell me is the correlation coefficient, r \lt 0, r = 0 or r \gt 0? Select the right answer.

## Question 3

Consider a coin that has a probability of landing on heads of 0.7. What is the probability of it landing on tails?

## Question 4

If we flip one coin with the probability of heads of 0.7followed by a fair coin, what is the probability of flipping heads followed by a tails?

## Question 5

What is the probability of having heads on the first flip or on the second flipif we have one coin with a probability of heads of 0.7 and a second coin with a probability of heads of 0.5? What is the probability that one of the two flips will result in heads?

Note:
"What is the probability that at least one of the two flips will result in heads?" is a more accurate statement. The "or" in P(\text{Heads on Flip1 or Flip2}) = ? is a logical or, i.e., (H,T), (T, H) and (H,H) satisfy the condition "Heads on Flip1 or Flip2".

## Question 6

We have two dice.One has 6 sides and one has 8 sides.We select which die to roll based on whether the flip of this coin is heads, in which case was roll the 6-sided die,or tails, in which case we roll the 8-sided die. What is the probability of rolling a 6? You can assume that the coins and dice are fair.

## Question 7

What is the probability that the coin flip was heads given that the roll was a 6?

Note:
A experimenter flips a fair coin. If the coin's outcome is Tails, the experimenter throws a 8-sided die. If the coin's outcome is Heads, the experimenter throws a 6-sided die. Given that the die's outcome is 6 (you don't know from which die), what's the probability that the coin's outcome was Heads? In the language of mathematics:

## Question 8

Given that we have a probability of rain on any given day of 0.2, what is the probability that over the course of a week it rains on exactly 2 days?

## Question 9

Given that we have a probability of rain of 0.2 on a given day, what is the probability of having rain on at least two days during the week?

## Question 10

A common measure of intelligence, IQ, is distributed with a mean of 100 and a standard deviation of 15. What is the standard score of an IQ of 130?

## Question 11

Consider a ball that is kicked by a mean of 10 feet in this directionand with a standard deviation of 1 foot. It is then kicked back in the opposite direction towards where it started by 5 feet,but this time with a standard deviation of 0.5. What are the mean and standard deviation of this distribution of the distance between the initial position and the final position?

## Question 12

In a population with a mean height of 70 inchesand a variance of 25,what are the mean and variance of the distribution of heights in centimeters? Recall that there are 2.54 cm per inch.

Note:
The given table is slightly wrong (incomplete to be more accurate) regarding the units. A more descriptive table would be:

 Height Distribution \mu \sigma^2 Value Unit Value Unit 70 inches 25 inches^2 ? cm ? cm^2

All is being asked is a unit conversion for \mu (from inches to cm) and \sigma^2 (from inches^2 to cm^2), i.e., if you change units for \mu (pretty much straightforward), how does the variance change?.

## Question 13

For a coin that's flipped 10,000 timeswith 4,950 of those flips resulting in heads,what is the 90% confidence interval for the probability of the coin landing on heads?

Note:
The TA did not use the same notation for confidence interval used in the lectures. There are two ways of specifying a confidence interval:

1. \mu \pm CI, e.g.: 1 \pm 0.01, if \mu = 1 and CI = 0.01 (Notation used in the lectures).
2. (\mu - CI) - (\mu + CI), e.g.: 0.99 - 1.01, if \mu = 1 and CI = 0.01 (Notation used by the TA).

The grader expects the second notation (2).

## Question 14

Given the following set of 10 range measurements, what is the 95% confidence interval for the actual distance?

Note:

 Distance (cm) 0.79 0.70 0.73 0.66 0.65 0.70 0.74 0.81 0.71 0.70

If you'd like to do your computations using Python instead of a calculator, copy this:

data=[0.79,0.70,0.73,0.66,0.65,0.70,0.74,0.81,0.71,0.70]

## Question 15

For this data set an observation of 0, 0 for x and y,of 1, 2, and of 2, 2, what is the least squares regression using the equation y = bx + a.Please provide b, the slope, and a, the intercept.

## Question 16

Rank the following four scatter plots by their correlation coefficient.One should have the lowest coefficient.Four should have the highest. Note that you're ranking by the coefficient itself, not the absolute value, so sign does matter.