Statistical Analysis

Question 1

In a lottery the probability of the jackpot prize being won is 1/60.

a) What is the probability that the jackpot will be won in 4 consecutive draws?
b) How many consecutive draws need to be made for there to be a greater than 98% chance that at least one jackpot prize will have been won.

Answer 1

a) 60^(-4)
b) 233

Question 2

Jack and Ben have been tracking their success rate of converting goals in their rugby games. Jack converts 70% of his goals and Ben converts 60%. At a recent home game, both get a kick, but only one converts his goal. What is the probability that it was Ben?

Answer 2

= 0.46/0.18
​
≈ 0.3913

= 39.13%

Question 3

What does P(X=x) mean?

Answer 3

Probability that a random variable X takes the value of x

Question 4

Which type of experiment has one possible outcome?

Answer 4

Deterministic Experiment

Question 5

Which type of experiment has more than one possible outcome?

Answer 5

Random Experiment

Question 6

What is p(x)

Answer 6

P(X=x)

Question 7

How is expected value denoted/written in math?

Answer 7

E(X)

Question 8

Formula of E(X) using weighted mean?

Answer 8

E(X) = Σxp(x)

Question 9

Formula for mean (μ)?

Answer 9

μ = Σxp(x)

Question 10

Variance Formula?

Answer 10

Var(X) = Σ(x-μ)²p(x)

Question 11

Variance Formula?

Answer 11

Var(X) = E((X-μ)²)

Question 12

Variance Formula?

Answer 12

Var(X) = Σx²p(x)-μ²

Question 13

Variance Formula

Answer 13

Var(X) = E(X²)-μ²

Question 14

Standard Deviation Formula?

Answer 14

σ = √(Var(X))

Question 15

How is relative frequency written?

Answer 15

f_r

Question 16

How is the mean denoted in sampling?

Answer 16

x̄

Question 17

How is variance written in sampling?

Answer 17

s²

Question 18

How is standard deviation written in sampling?

Answer 18

s

Question 19

A study of fatal car accidents found that out of 2345 car accidents in 2018, 1980 of them were due to speed. Of those car accidents that were due to speed, 1452 of them were caused by drivers under the age of 25. A total of 1617 accidents were caused by drivers under the age of 25.

What is the probability that a fatal accident by a driver over 25 was not caused by speed?

Answer 19

0.27

Question 20

Billy and Tom take penalty kicks in rugby. Billy converts 60% of the kicks he takes, and Tom converts 55% of his kicks.

Last week, Billy and Tom each had one kick, but only one of them converted. What is the probability that Billy made the successful kick?

Answer 20

27/49

Question 21

Penny plays a game by rolling 2 red dice and 1 blue die. She wins if the blue die lands inside the values of the red dice. For example, if the red dice land on 1 and 4, Penny wins if the blue die lands on 2 or 3.

What is the probability that Penny wins the game?

Answer 21

5/27