Probability and random variables
Skittles factories typically produce a range of number of candies per pack of fun size Skittles: 13, 14, 15, 16, 17. Here's the distribution of the probabilities of numbers of Skittles per pack:
Value: 13 14 15 16 17
Probability: 0.094 0.246 0.318 X 0.053
The probability of a pack having 16 Skittles.
What is 0.289?
Brian is sharp shooter on the court. He is shooting 5 free throws to win a bet for $10. He is an 79% free throw shooter. The table below shows the probability of getting exactly X shots made.
Shots made (X): 0 1 2 3 4 5
Probability: ~0 0.008 0.058 0.217 0.409 X
The probability of Brian making all 5 free throws.
Binompdf (5, .79, 5)
What is 0.308?
Mean, Standard Deviation, Variance
The metrics that change when being multiplied/divided by a number.
What is all of them?
The labels for a normalcdf calculation.
What is low, up, mean, and standard deviation?
The difference between binomial and geometric distributions.
What is binomial has a fixed number of trials and geometric doesn't?
Skittles factories typically produce a range of number of candies per pack of fun size Skittles: 13, 14, 15, 16, 17. Here's the distribution of the probabilities of numbers of Skittles per pack:
Value: 13 14 15 16 17
Probability: 0.094 0.246 0.318 X 0.053
The type of variable Skittles is (discrete or continuous). Explain.
What is discrete because the data has a fixed set of values with gaps in between (whole numbers)?
Brian is sharp shooter on the court. He is shooting 5 free throws to win a bet for $10. He is an 79% free throw shooter. The table below shows the probability of getting exactly X shots made.
Shots made (X): 0 1 2 3 4 5
Probability: ~0 0.008 0.058 0.217 0.409 .308
The BINS conditions the data follows.
What is:
B - Binary, I - Independent, N - Fixed number, S - Probability of Success is Same on each trial?
Mean, Standard Deviation, Variance
The metrics that don't change when being added or subtracted by a number.
What is mean?
The percentage of a normal curve that is one standard deviation above the mean.
What is 34%?
Shai Gilgeous-Alexander is hurt after Wembanyama knocked him out in the playoffs. To get revenge, he challenges Wemby to 1-on-1 until he can beat him. The probability that SGA wins a game is 10.9%. Assume each game is independent.
The expected number of games played.
1/p
What is 9.174 games?
Skittles factories typically produce a range of number of candies per pack of fun size Skittles: 13, 14, 15, 16, 17. Here's the distribution of the probabilities of numbers of Skittles per pack:
Value: 13 14 15 16 17
Probability: 0.094 0.246 0.318 X 0.053
The probability of getting less than 17 Skittles in a pack.
What is 0.947?
Brian is sharp shooter on the court. He is shooting 5 free throws to win a bet for $10. He is an 79% free throw shooter. The table below shows the probability of getting exactly X shots made.
Shots made (X): 0 1 2 3 4 5
Probability: ~0 0.008 0.058 0.217 0.409 .308
The standard deviation of the dataset.
Square root (npq)
What is 0.911 shots?
The length of the books that Peyton has written so far this year has a mean of 80,000 words with a standard deviation of 10,986 words. The length of the books that Peyton wrote last year has a mean of 65,000 with a standard deviation of 8,374 words.
The combined mean number of words Peyton writes.
What is 145,000 words?
The amount of time Mauris competes against Brian in Uno in a given round is normally distributed with a mean of 48 minutes and a standard deviation of 7.3 minutes.
The probability that a game is longer than 46 minutes.
normalcdf (46, 99999, 48, 7.3)
What is 0.608?
Shai Gilgeous-Alexander is hurt after Wembanyama knocked him out in the playoffs. To get revenge, he challenges Wemby to 1-on-1 until he can beat him. The probability that SGA wins a game is 10.9%. Assume each game is independent.
The probability that Shai can win in the 5th game.
geometpdf (.109, 5)
What is 0.069?
Skittles factories typically produce a range of number of candies per pack of fun size Skittles: 13, 14, 15, 16, 17. Here's the distribution of the probabilities of numbers of Skittles per pack:
Value: 13 14 15 16 17
Probability: 0.094 0.246 0.318 0.289 0.053
The expected number of Skittles in a pack.
What is 14.961?
Brian is sharp shooter on the court. He is shooting 5 free throws to win a bet for $10. He is an 79% free throw shooter.
The probability of Brian making at most 3 shots.
Binomcdf (5, .79, 3)
What is 0.283?
The length of the books that Peyton has written so far this year has a mean of 80,000 words with a standard deviation of 10,986 words. The length of the books that Peyton wrote last year has a mean of 65,000 with a standard deviation of 8,374 words.
The combined standard deviation of words Peyton writes.
What is 13813.619?
The amount of time Mauris competes against Brian in Uno in a given round is normally distributed with a mean of 48 minutes and a standard deviation of 7.3 minutes.
The probability that a game lasts between 47.3 and 50.6 minutes AND the interpretation in context.
normalcdf (47.3, 50.6, 48, 7.3)
What is 0.177 and there is a 17.7% chance that an Uno game lasts between 47.3 and 50.6 minutes.
Shai Gilgeous-Alexander is hurt after Wembanyama knocked him out in the playoffs. To get revenge, he challenges Wemby to 1-on-1 until he can beat him. The probability that SGA wins a game is 10.9%. Assume each game is independent.
The probability that SGA wins in 17 games or less.
geometcdf (.109, 17)
What is 0.859?
Skittles factories typically produce a range of number of candies per pack of fun size Skittles: 13, 14, 15, 16, 17. Here's the distribution of the probabilities of numbers of Skittles per pack:
Value: 13 14 15 16 17
Probability: 0.094 0.246 0.318 X 0.053
The standard deviation and its interpretation.
What is 1.059 and the average distance from a Skittle pack's mean number of 14.961 Skittles is 1.059 Skittles?
Brian is sharp shooter on the court. He is shooting 5 free throws to win a bet for $10. He is an 79% free throw shooter.
The probability of Brian making 2 or more shots.
1 - Binomcdf (5, .79, 1)
What is 0.992?
The length of the books that Peyton has written so far this year has a mean of 80,000 words with a standard deviation of 10,986 words. The length of the books that Peyton wrote last year has a mean of 65,000 with a standard deviation of 8,374 words.
The new standard deviation if the data from this year was transformed into the line y = 9872 + 83x.
What is 911838 words?
The amount of time Mauris competes against Brian in Uno in a given round is normally distributed with a mean of 48 minutes and a standard deviation of 7.3 minutes.
The standardized score of a game that is 47.4 minutes long.
(observed-expected)/standard deviation
What is z=-0.082?
Shai Gilgeous-Alexander is crying because he can't beat Wemby, so he gets Lu Dort to foul him hard to even the odds. The probability that SGA wins a game now is 30.872%. Assume each game from now on is independent.
The probability that Wemby loses on the 11th game.
geometpdf (.30872, 11)
What is 0.008?