Statistics and Probability Answers

The total area under the relative frequency polygon equals 1 when the interval size is 1.

True
False

The total area under a probability density polygon equals 1.

True
False

Heights of students in your class.

1 Continuous


2 Discrete

An automobile manufacturer is concerned about a fault in the braking mechanism of a particular model. The fault can, on rare occasions, cause a catastrophe at high speed. The distribution of the number of cars per year that will experience the catastrophe is a random variable with variance = 5.
(a) What is the probability that at most total 30 cars in 35 year will experience a catastrophe?
(b) What is the probability that average less than 3 cars in 35 year will experience a catastrophe?

The probability that a student belongs to a club is P(C)=0.4. The probability that a student works part time is P(PT)=0.5. The probability that a student belongs to a club AND works part time is P(C and PT)=0.05. What is the probability that a student belongs to a club OR works part time?

Consider the de Mérés game which is played as follows: In Game 1, there are 4
rolls of a die and you win with at least one 6. In Game 2, there are 24 rolls of two dice and you
win by at least one pair of 6’s rolled.How many possible outcomes could be realized for
(a) Game 1
(b) Game 2
How many elements are in the event (E1) of getting an outcome without a 6 for
(a) Game 1
(b) Game 2

Consider an experiment of rolling a fair die 5 times. How many elements are in the event space (E3) of getting an outcome where first number
could be (2 or 3) middle number could be either (5,6 or 3) and last number must be 4?

The following probability distribution graph has a missing value for the outcomes of x = 2 and x = 6. Note that x = {1, 2, 3, 4, 5, 6}.
Furthermore, P(x = 2) + 3P(x = 6) = 0.7
Determine the probability outcomes of both P(x = 2) and P(x = 6). Show all your work.
GRAPH:

0.4-

0.3- ---

0.2- ---
---
0.1-
1 2 3 4 5 6 2&6 are blank.

NHL mega-superstar Auston Matthews scores on 15% of his shots.
What is the expected waiting time before he misses a shot?

Brooke walks to the convenience store everyday and passes a hot dog vendor that has a
30% chance of saying “Hello” to her. After she buys the newspaper, she takes a different
route home and does not see the vendor again until the next day.
a) What is the probability that the vendor will
say “Hello” exactly three times in the next
two weeks?
b) What is the probability that the vendor will not
say “Hello” until the 10th day?