Probability Distribution
Expected Value
Binomial Distribution
Normal Distribution
Z-Scores
100
Does this table represent a probability distribution?
What is yes?
100
Jake the dog delivers pizzas for a local dog-friendly pizzeria. For each delivery, he earns a tip based on customer satisfaction. The probabilities are listed below: 10% chance he makes $0, 30% chance he makes $2, 40% chance he makes $5, and 20% chance that he makes $10. What is the expected value?
What is $4.60?
100
A squad of stormtroopers has a 30% chance of hitting their target with each shot. If one stormtrooper fires 5 times, what is the probability he hits the target exactly 2 times?
What is 0.3087?
100
The Rivendell elves' archery accuracy follows a normal distribution with a mean score of 90 bullseyes and a standard deviation of 5. What percent of elves score less than 95 bullseyes?
What is 84%?
100
Tony Stark takes a tech assessment. The class average is 80 with a standard deviation of 5. If Tony scores a 90, what is his Z-score?
What is 2?
200
Does this table represent a probability distribution?
What is no?
200
Jake the dog plays a game where he picks a random item from his magical hat. Each item has a different value. A squeaky toy values at $1, and bone values at $5, and a hamburger values at $20. There are 20 squeaky toys, 13 bones, and 8 hamburgers. What is the expected value?
What is $5.98?
200
R2D2 is testing a new sensor with a 90% success rate. If it's tested 8 times, what is the probability it works at most 7 times?
What is 0.57?
200
/The number of biscuit pieces eaten by the hobbits per day is normally distributed with a mean of 6 pieces and a standard deviation of 1.5. What is the probability that a randomly selected hobbit eats between 3 and 7.5 pieces?
What is 81.5%?
200
Steve Rogers runs a speed test. The mean running speed is 21 km/h with a standard deviation of 2. If Cap runs at 34 km/h, what's his Z-score?
What is 6.5?
300
Find P(x=5)
What is 0.16?
300
Jake is training younger pups in the art of battle. He gets paid per successful training session, but payment varies depending on the skill level of the trainee. Five of his students are beginners, three are intermediate, and two are experts. Beginner students pay him $25, intermediate students pay him $35, and expert students pay him $50. What is the expected value of Jake's training sessions?
What is $33?
300
Obi-Wan has a 74% success rate using mind tricks. During a field test of 10 tries, what is the probability she succeeds at least 9 times?
What is 0.22?
300
The height of orcs is normally distributed with a mean of 160 cm and a standard deviation of 8 cm. What percentage of orcs are between 136 cm and 176 cm?
What is 97.35%?
300
Hawkeye hits a moving target in an archery simulation. The mean score is 85 with a standard deviation of 7. If he gets a Z-score of 1.5, what was his actual score?
What is 95.5?
400
Find P(x>2)
What is 0.4?
400
Jake pays $15 to enter a fencing tournament. If he wins he earns $50, if he ties he earns nothing, and if he loses he has to pay his opponent $10. He has a 55% chance of wining, a 20% chance of tying, and a 25% chance of losing. What is the expected value?
What is $13?
400
A rebel pilot has a 65% chance of successfully dodging enemy blaster bolts. If they face 12 incoming shots during a dogfight, what is the probability they dodge more than 8 of them?
What is 0.347?
400
The height of orcs in Sauron's army is normally distributed with a mean of 143 cm and a standard deviation of 7 cm. The army has 5,000 orcs. How many orcs are shorter than 129 cm?
What is 125 orcs?
400
Bruce Banner measures gamma readings during an experiment. The Z-score is -2, the standard deviation is 10, and his gamma level was 100 units. What was the mean gamma level recorded?
What is 120 units?
500
Find P(x=1) or P(x=2)
What is 0.6?
500
Jake pays $10 to enter a hotdog eating contest. If he wins first, he earns $50. If he wins second, he wins $25. If he wins third, he wins $10. He has a 10% probability of first place, a 23% probability of second place, and a 29% probability of third place. What is the expected value?
What is $3.65?
500
A cloning facility produces elite troopers with a 91% success rate. If 118 clones are created, what is the probability that less than 12 are defective?
What is 0.627?
500
Archery scores are normally distributed with a mean of 88 and a standard deviation of 5. There are 120 elves competing. How many elves scored more than 78?
What is 117 elves?
500
In a covert agility test, Black Widow scores 42 points. The average score among SHEILD agents is 36, and her Z-score is 1.5. What is the standard deviation of these scores?
What is 4 points?