Unit 3 Quiz Review
1) If a dataset is normally distributed with mean 50 and standard deviation 5, what is the left-tail area for the value 57? In other words, what proportion of data in the set is below 57? Initialize the value of 'leftTail' below.
2) If a dataset is normally distributed with mean 100 and standard deviation 8, what is the area between 105 and 110? In other words, what proportion of data in the set is between 105 and 110? Initialize the value of 'middle' below.
3) Suppose a dataset is normally distributed with mean 70 and standard deviation 11. What score in the dataset is at the 90th percentile? This is the score X such that 90% of the scores in the dataset are less than X. Initialize the value of 'x' below.
4) Suppose the length of time Android phone batteries last is normally distributed with mean 5 years and standard deviation 1.4 years. If Android sold 40 million phones 3 years ago, what is our estimate for how many of those phones' batteries that have died?
Initialize the value of 'numberDead' below.
5) Suppose there is a game of chance played with rules listed below:
A person pays $10 to play the game.
A person rolls a six-sided fair die. If the result is 6, the person wins a prize of $20.
If a 6 is NOT rolled, the person flips a coin. If the result is heads, the person wins a prize of $15. If the result is tails, the person wins nothing.
Note: If a person pays $10 to play and wins a prize of $20, the profit of the game is $20-$10 = $10.
We want to figure out if playing this game is worth the risk. One metric used to determine this is to determine how much profit a person would win on average by playing this game MANY times. We will show 5 trials below.
Trial 1: dieRoll = 6
Trial 2: dieRoll = 2, coinFlip = heads
Trial 3: dieRoll = 5, coinFlip = tails
Trial 4: dieRoll = 1, coinFlip = heads
Trial 5: dieRoll = 6
What is our estimate of the average profit made from playing the game (based on the 5 trials)? Appropriately initialize the variable 'avg' to represent our estimate.
6) Assuming that Lebron has a 73.4% chance of making a free throw on any attempt, estimate the probability that Lebron would miss two or more free throws with three attempts.
random() returns a value in the interval [0,1)
Let anything less than or equal to .734 indicate a make, and greater than .734 as a miss.
Trial 1: .791, .555, .988
Trial 2: .468, .332, .712
Trial 3: .811, .025, .795
Trial 4: .356, .665, .612
Trial 5: .199, .024, .897
What is our estimate for the probability that Lebron will miss 2 or more free throws out three (based on the five trials)? Appropriately initialize the value of 'proportion' to represent our estimate.
7) To “Get out of Jail” in Monopoly a player has to roll doubles on a pair of dice, which means both dice result in the same number.
Estimate the probability that you would have to roll less than 6 times before you obtain doubles. Five trials are shown below:
Trial 1: (6, 4), (5, 4), (2, 2)
Trial 2: (3,3)
Trial 3: (1,2), (3,4), (5,2), (6,4), (2,3), (3,1), (3,3)
Trial 4: (3,5), (4, 2), (4,3), (6,6)
Trial 5: (2,3), (3,5), (1,1)
Based on our five trials, appropriately initialize the value of 'proportion' to represent our estimate.
8) What is 6! Initialize the value of 'nFactorial' below to represent the value.
9) What is 7C3? Initialize the value of 'combination' below.
10) What is 7P3? Initialize the value of 'permutation' below.
11) Suppose we were to roll a fair die 5 times. What is the probability we would obtain a "6" exactly one time? The value for 5C1 = 5.
Appropriately initialize the value for 'binomialpdf' below.
12) Suppose we have a 70% chance of winning a certain game of chance. We plan to play the game 12 times. What is the probability we win exactly 8 games? 12C8 is 495.
Appropriately initialize the value for 'binomialpdf' below.
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