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Business Stats Midterm > Midterm 2 > Flashcards

Midterm 2 Flashcards

1
Q

Define Probability

A

The “chance” of an event occurring when the experiment is conducted

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2
Q

Explain what the P(A) notation means in the context of probability.

A

P(A) = the chance that event A occurring.

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3
Q

Define the terms “event” and “outcome” in probability.

A

An event is a collection of one or more outcomes of an experiment.

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4
Q

What are mutually exclusive events? Provide an example.

A

events that cannot occur simultaneously. Flipping a coin and getting both heads and tails.

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5
Q

How do you calculate the standard deviation? There are 5 steps.

A
  1. Calculate the Mean
  2. Subtract the Mean from each of the values
  3. Square the Results
  4. Add up all results and divide by amount of results
  5. Take the Square Root
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6
Q

What is a continuous random variable? What’s an example?

A

A continuous random variable is has potentially equal an uncountably infinite amount of different values. Examples of this are time and height. These values are decimals or fractions as they have infinite values.

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7
Q

What is a discrete random variable? What’s an example?

A

A discrete random variable is defined in such a way that it can only possible equal a finite or countable amount of different values. Examples of this is the amount of heads flipped in an experiment when flipping coins.

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8
Q

What is a random variable?

A

These variables also represent quantities or numerical values, but the difference is that the quantity it represent depends on
the outcome of an experiment.

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9
Q

Differentiate between discrete and continuous random variables.

A

Discrete values must be integers but continuous values can be decimals and fractions.

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10
Q

How do you calculate mean? (expected value)

There are two steps.

A

1) Multiply each value by its probability
2) Sum the products
This can be done easily using the =sumproduct function in Excel

COLUMN X COLUMN, NOT ROW BY ROW!

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11
Q

Explain what a probability distribution is

A

A probability distribution lists all of the values a random variable can equal next to their probabilities

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12
Q

Define Binomial Probability

A

A binomial probability question is a probability question of the general form “What is the probability something happens a certain number of times during a multi-step experiment?”

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13
Q

What is the formula for calculating binomial probabilities?

A

=binom.dist(number_s, trials, probability_s, cumulative)

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14
Q

Where is the number_s fit into the binom.dist function and what does number_s mean? What letter is it denoted as in the alternative equation?

A

This calculates the number of successes you want to happen. This is the letter x

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15
Q

Where does the trials fit into the binom.dist function and what does trials mean? What letter is it denoted as in the alternative equation?

A

amount of trials ( the total amount you are doing something out of ). This is letter n.

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16
Q

Where does the probability_s fit into the binom.dist function and what does probability_s mean? What letter is it denoted as in the alternative equation?

A

this is the chance that something will happen, ONLY a percentage/decimal. This is letter p.

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17
Q

What is the difference between TRUE and FALSE in a binom.dist function?

A

TRUE: probability of a success occurring OR LESS
FALSE: EXACT probability of a success occurring

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18
Q

What are the 4(????) conditions that make a probability distribution binomial?

A

Criteria 1: The experiment must be a multi-step experiment. We call each step a trial, and the number of trials n
Criteria 2: Each trial must be identical and independent
Criteria 3: Each trial has a notion of success (p) and failure (q).
Criteria 4: “What is the probability of observing a certain amount of successes during our n trials??” must be answered

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19
Q

Shaq has a 52.7% free-throw average, meaning that when he attempts a free-throw, he has a 52.7% chance to successfully
make it. If he attempts 14 free-throws during a game, what is the probability he makes less than 9 of them?

A

=BINOM.DIST(8,14,52.7%,TRUE)

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20
Q

Define PDF.

A

PDF stands for Probability Density Function is a way to show probabilities for continuous outcomes, focusing on ranges of outcomes rather than specific numbers, and it uses the concept of “area under the curve” to talk about probabilities

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21
Q

How do you calculate the area under a PDF?

A

You use the norm.dist function. If it is between 2 points, you use (=NORM.DIST(x2, mean, st dev, TRUE) - NORM.DIST(x1, mean , stdev, TRUE)).The area will ALWAYS equal one.

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22
Q

What does the area under a PDF represent?

A

The area under a pdf between two values of X represents the probability that the random variable will equal a number between those two values.

23
Q

What will we NEVER use in a norm.dist or a norm.s. dist function?

A

We will never have the cumulative value set to FALSE.

24
Q

What are the properties of the normal distribution curve?

A

The further you get from the mean of the bell curve, the less common those values are to occur. The height of a normal distribution decreases as it gets farther from the mean.

25
Q

What does it mean for a dataset to be normally distributed?

A

If a random variable is “normally distributed”, it means it has a symmetric bell-curve as its pdf.

26
Q

What is a Z-score, and how does it relate to normal distribution?

A

Z-scores are used for assessing how unusual a measurement is within a dataset. You can use the standard normal distribution to find out the probability of that score occurring or the probability of a score being lower or higher than that value.

27
Q

What is the difference between NORM.DIST and NORM.INV?

A

Both use mean and standard deviation to compute answers. But, Norm inv is the inverse function and uses percentages to calculate z-scores. Norm dist is used to calculate a value that corresponds to x.

28
Q

What is the standard normal?

A

The standard normal functions exactly like a regular normal distribution. It is referred to as the capital letter Z.

29
Q

How would I compute the probability that a value is between the standard deviation of -1 and 1? What functions would I use?

A

=NORM.S.DIST( 1, TRUE) - NORM.S.DIST( -1, TRUE)

30
Q

If you are expected to find a z-score of 7 and you are given the mean of 2.5 and a standard deviation of 1.012, how do you calculate the amount of standard deviations away from the mean?

A

The z-score would be put into the equation (value - mean) / stdev. This would get you ( 7 - 2.5) / 1.012.

31
Q

What is the mean and standard deviation of a standard normal distribution?

A

the mean (µ) = 0 and the stdev (σ) = 1.

32
Q

How is equal outcome calculated?

A

P(event) = (Number of outcomes in the event) / (total number of outcomes in experiment)

33
Q

Countably infinite

A

infinite possibilities, but locked into whole numbers

34
Q

Uncountably infinite

A

infinite possibilities with the possibility of decimal precision

35
Q

What will the probability of a random variable in all trials always equal?

A

It will ALWAYS equal 100% or 1

36
Q

What is the function used to calculate a normal distribution?

A

=norm.dist(x, mean, standard_dev, TRUE)

37
Q

Brad (a man) is taller than 70% of other men. For men, the mean = 69.1 inches and stdev = 2.5 inches. How would this question be solved?

A

=NORM.INV(70%, 69.1, 2.5)

38
Q

How do I calculate the probability of this normal distribution (mean = 70 and stdev = 12) having a value between 60 and 80?

A

P(60 < X < 80) = P(X < 80) - P(X < 60) =

=NORM.DIST(80,70,12,TRUE) - NORM.DIST(60,70,12,TRUE)

39
Q

What does =BINOM.DIST(x, n, p, FALSE) compute?

A

It computes the probability of observing EXACTLY x successes during our n trials with probability of success p

40
Q

What does =BINOM.DIST(x, n, p, TRUE) compute?

A

It computes the probability of observing x or less successes during our n trials with probability of success p

41
Q

What does
=BINOM.DIST(x - 1, n, p, TRUE) compute?

A

It computes the probability of observing less than x successes during our n trials with probability of success p (Note: ‘Less than x’ does not include x, hence why we use x-1)

42
Q

What does = 1 -BINOM.DIST(x, n, p, TRUE) compute?

A

The above returns the probability of observing more than x successes during our n trials with probability of success p

43
Q

What does
= 1 -BINOM.DIST(x-1, n, p, TRUE)
compute?

A

It computes the probability of observing atleast x successes during our n trials with probability of success p

44
Q

What does =BINOM.DIST(x, n, p, TRUE) - BINOM.DIST(y-1, n, p, TRUE) compute?

A

It computes the probability of observing the distance of the successes between the values x and y during our (N) trials.

45
Q

How do you compute the mean?

A

Mean = Expected Value = n * p

46
Q

How do you compute the standard deviation and the variance?

A

Variance = n * p * (1-p)
Stdev = Sqrt(Variance)

47
Q

TRUE OR FALSE: The total area under the pdf of any continuous random variable is 1.00

A

TRUE: The total area under the pdf represents the total probability of all outcomes, which must sum up to 1 (or 100%).

48
Q

TRUE OR FALSE: For any continuous random variable X, and potential value a, P(X < a) = P(X ≤ a)

A

FALSE: In the case of continuous random variables, the probability that X is exactly equal to any specific value a is 0.

49
Q

TRUE OR FALSE: Assume X is a uniform random variable, bounded below by 5 and above by 10. X can then potentially only equal 6 different values, namely {5, 6, 7, 8, 9, 10}

A

FALSE: It can be any decimal or fractional number between 5 and 10.

50
Q

TRUE OR FALSE: The curve of the pdf of a continuous random variable can potentially dip below the x-axis when graphed

A

FALSE: The probability cannot dip below the X -axis because probability cannot be negative.

51
Q

TRUE OR FALSE: Assume we define a random variable as “The weight of a random adult male gorilla”. This random variable, conceptually, is likely uniform

A

TRUE: it is uniform because the distribution of weights for a gorilla will likely fall around the same values.

52
Q

What is the equation for a uniform dataset?

A

(d - c) / ( b - a)

53
Q

How do you calculate the mean of a uniform dataset?

A

( a + b ) / 2

54
Q

How do you calculate the variance of a uniform dataset?

A

(b - a)^2 / 12

Business Stats Midterm (3 decks)

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