#1
The heights of adult males are normally distributed with the following parameters
Mean=70 Standard deviation=3
Task 1: The average NBA player is 6’7″, or 79 inches tall. What is the probability that if you select an adult male at random, they will be as tall as or taller than the average NBA player? (that is, greater than 79 inches tall)
Task 2: What is the probability that a random adult male is under 6′, or 72 inches tall?
Task 3: What is the probability that a random adult male is between 67 and 74 inches tall?
include excel funtions and plug in data
#2
In the popular table top game, Dungeons and Dragons, many events are decided by the roll of a 20 sided die.
Suppose that a Wizard and a Barbarian are stuck in a pit. If at least one of the two can climb out of the pit, they will be able to go get help. They could either both try to climb out of the pit independently, or they could help each other.
Task 1: Suppose the party Wizard needs to climb over a wall. The Wizard is not particularly strong, and needs a 16 or higher on the die to climb over the wall. What is the probability that the Wizard makes it over the wall?
A common mechanic in DnD is “advantage”. If a character is granted advantage, say by some sort of helping action, then they get to roll two dice and take the better result. In this case, if either of the two dice succeed, then the attempt succeeds
Task 2: Suppose the Wizard enlists the help of the party Barbarian to get over the wall. The Wizard then can roll two dice, and only needs a 16 on at least one of the two dice. What is the probability that the Wizard gets over the wall with advantage?
Characters can also get disadvantage, which is rolling two dice and taking the worse result. In this case both of the dice would have to be a success in order for the attempt to succeed.
Task 3: Suppose the Wizard recently sprained their ankle, and there is no nearby Barbarian to help. What is the probability that the Wizard can climb the wall with disadvantage?
Task 4: After the Wizard climbs over the wall, they find themselves face to face with 5 goblins. The Wizard makes a spell attack on each goblin that will hit if the Wizard rolls at least an 8. What is the probability that the Wizard will hit at least 3 of the 5 goblins?
Include EXCEL FUNCTIONS and plug in data
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