This Jeopardy is Half-

normal

Therefore, it must be half abnormal...?

Sections B25-28

Rules

• I’ll randomly pick groups to select a question. Then everyone can work on it.

• Raise your hand to announce the answer. First group to get the correct

answer gets full points.

• If your answer is half-correct I’ll give you half the points and the other half

continues to be open to everyone else.

• I’ll reveal the answer once the question is correctly answered.

Rules on the

road

The guessing

game

Approximately

normal...

Teams and

Competitions

100 100 100 100

200 200 200 200

300 300 300 300

400 400 400 400

Rules on the Road (100)

Of the people getting their driving license at the DMV this year, 30% pass the driving test in

one go and the rest needed more than 1 try. 1% of those who passed the test in one go had a

traffic rule violation in the next 6 months, whereas for the other group it was 0.5%. Are passing

the test in one try (or not) and having a traffic violation in the next 6 months independent?

Rules on the Road (200)

Of the people getting their driving license at the DMV this year, 30% pass the driving test in one go and

the rest needed more than 1 try. 1% of those who passed the test in one go had a traffic rule violation in

the next 6 months, whereas for the other group it was 0.5%. What is the probability that a person passed a

test in one go, and had traffic violation in the next 6 months?

Rules on the Road (300)

Of the people getting their driving license at the DMV this year, 30% pass the driving test in one go and

the rest needed more than 1 try. 1% of those who passed the test in one go had a traffic rule violation in

the next 6 months, whereas for the other group it was 0.5%. If a random driver who is licensed this year

is picked, what is the probability that (s)he has a violation (within 6 months after getting the license)?

Rules on the Road (400)

Of the people getting their driving license at the DMV this year, 30% pass the driving test in one go and

the rest needed more than 1 try. 1% of those who passed the test in one go had a traffic rule violation in

the next 6 months, whereas for the other group it was 0.5%. Given that a driver has a violation, what is

the probability that (s)he passed the driving test in 1 go? (Answer as decimal or fraction.)

The Guessing Game (100)

It’s Trivia Night at the Prairie Fire. There are 5 questions, and the host is gracious enough to give you 4

choices per question. Get 2 or more correct and you get a free cake. But you were literally born yesterday,

so you don’t know anything and can only guess each question randomly. Let X be the number of

questions you answer correctly. What distribution does X follow, and what are its parameters?

The Guessing Game (200)

It’s Trivia Night at the Prairie Fire. There are 5 questions, and the host is gracious enough to give you 4

choices per question. Get 2 or more correct and you get a free cake. But you were literally born yesterday,

so you don’t know anything and can only guess each question randomly. What is the probability you get all

of them wrong and embarrass yourself ?

The Guessing Game (300)

It’s Trivia Night at the Prairie Fire. There are 5 questions, and the host is gracious enough to give you 4

choices per question. Get 2 or more correct and you get a free cake. But you were literally born yesterday,

so you don’t know anything and can only guess each question randomly. What is the probability that you

don’t get free cake?

The Guessing Game (400)

It’s Trivia Night at the Prairie Fire. There are 5 questions, and the host is gracious enough to give you 4

choices per question. Get 2 or more correct and you get a free cake. But you were literally born yesterday,

so you don’t know anything and can only guess each question randomly. What is the probability that you

get the free cake?

Approximately Normal...(100)

A company manufactures umbrellas. A recent machine failure causes 10% of

umbrellas newly manufactured to be missing their handles. We randomly

sample 20 umbrellas. If we want to find the probability that 5 or more are

missing their handles, can we use a normal approximation? Why or why not?

Approximately Normal...(200)

A company manufactures umbrellas. A recent machine failure causes 10% of

umbrellas newly manufactured to be missing their handles. We randomly

sample 400 umbrellas. What is the mean and standard deviation of the number

of umbrellas missing their handles, among these 400?

Approximately Normal...(300)

A company manufactures umbrellas. A recent machine failure causes 10% of umbrellas newly

manufactured to be missing their handles. We randomly sample 400 umbrellas. What is the (approximate)

probability that less than 30 are missing their handles?

Approximately Normal...(400)

A company manufactures umbrellas. A recent machine failure causes 10% of umbrellas newly

manufactured to be missing their handles. We randomly sample 400 umbrellas. What is the (approximate)

probability that between 30 and 55 are missing their handles?

Teams and Competitions (100)

In a relay race, Jim is the first runner and Tom is the second. The time it takes for Jim to run to Tom is

normally distributed with mean 120 seconds with standard deviation of 4 seconds, and the time for Tom

to run to the next runner is normally distributed with mean 140 seconds with standard deviation of 3

seconds. If the two run-times are independent, and the passing of the baton is instantaneous, then the

time it takes for the baton to travel from Jim to the 3rd runner has a _____________ distribution.

Teams and Competitions (200)

In a relay race, Jim and Joe are first runners for competing teams. The time it takes Jim to reach the first

station is normally distributed with mean 120 seconds and standard deviation 4 seconds. Joe’s time is also

normally distributed with mean 110 seconds and standard deviation 7.5 seconds. If the two times are

independent, then the difference “Jim’s time – Joe’s time” has a _______________ distribution with

_________________ and _________________ (values of two parameters).

Teams and Competitions (300)

In a relay race, Jim is the first runner and Tom is the second. The time it takes for Jim to run to Tom is

normally distributed with mean 120 seconds with standard deviation of 4 seconds, and the time for Tom

to run to the next runner is normally distributed with mean 140 seconds with standard deviation of 3

seconds. If the two run-times are independent, and the passing of the baton is instantaneous, what is the

probability that the baton takes more than 270 seconds to travel from Jim to the 3rd runner?

Teams and Competitions (400)

In a relay race, Jim and Joe are first runners for competing teams. The time it takes Jim to reach the first

station is normally distributed with mean 120 seconds and standard deviation 4 seconds. Joe’s time is also

normally distributed with mean 110 seconds and standard deviation 7.5 seconds. If the two times are

independent, then what is the probability that Jim reaches the first station before Joe?

Thanks for playing!

• Good luck on the test!