Statistics and Probability Answers

Supposed that the z is the test statistics for hypothesis testing, calculate the value of the z for each of the following. Express your answer in 2 decimal places. µ = 77, σ = 6, n = 109, x̄ = 78.2

A sawmill makes boards that are used in construction projects. The board lengths of two-by-fours produced by this sawmill are uniformly distributed from 6 ft to 12 ft.
Question 1: Describe the graph of this distribution.
Question 2: Determine the probability that a board selected at random will be at least 10 ft long.

Suppose John writes down a single number that is in the range from 1 to 20, and Susan also writes down a single number in the range from 1 to 20. What is the probability that the number John wrote down will be higher than Susan’s?

A No Claims Discount system is operated by a car insurer. There are four levels of discount: 0%, 10%, 25% and 40%. After a claim-free year a policy holder moves up one level (or remains at the 40% level if they are already there). If a policy holder makes one claim in a year he or she moves down one level (or remains at the 0% level if already there). A policyholder who makes more than one claim in a year moves down two levels (or moves to or remains at the 0% level). Changes in level can only happen at the end of each year. The probability of a claim in any given month is assumed to be constant at 0.04 (i.e. 4%). At most one claim can be made per month and claims are assumed independent. Calculate the proportion of policyholders in the long run who are at the 25% level.

Fake news post count is it a qualitative nominal variable?

05) a) Tiger Funds Ltd. operates a number of mutual funds in high technology and in financial
sectors. Hussein Roberts is a fund manager who runs a major fund that includes a wide
variety of technology stocks. As fund manager he decides which stocks should be purchased
for the mutual fund. The compensation plan for fund managers includes a first-year bonus
for each stock purchased by the manager that gains more than 10% in the first six months it
is held. Of those stocks that the company holds, 40% are up in value after being held for two
years. In reviewing the performance of Mr. Roberts, they found that he received a first-year
bonus for 60% of the stocks that he purchased that were up after two years. He also received
a first-year bonus for 40% of the stocks he purchased that were not up after two years.
What is the probability that a stock will be up after two years given that Mr. Roberts received
a first-year bonus?

b) A restaurant manager classifies customers as regular, occasional, or new, and finds that of all
customers 50%, 40%, and 10%, respectively, fall into these categories. The manager found that
wine was ordered by 70% of the regular customers, by 50% of the occasional customers, and by
30% of the new customers.
I. What is the probability that a randomly chosen customer orders wine?
II. If wine is ordered, what is the probability that the person ordering is a regular
customer?
III. If wine is ordered, what is the probability that the person ordering is an occasional
customer?

04) a) In a campus restaurant it was found that 35% of all customers order vegetarian meals and that
50% of all customers are students. Further, 25% of all customers who are students order
vegetarian meals.
I. What is the probability that a randomly chosen customer both is a student and orders a
vegetarian meal?
II. If a randomly chosen customer orders a vegetarian meal, what is the probability that the
customer is a student?
III. What is the probability that a randomly chosen customer both does not order a
vegetarian meal and is not a student?
IV. Are the events “customer orders a vegetarian meal” and “customer is a student”
independent?
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V. Are the events “customer orders a vegetarian meal” and “customer is a student”
mutually exclusive?

c) An insurance company estimated that 30% of all automobile accidents were partly caused by
weather conditions and that 20% of all automobile accidents involved bodily injury. Further, of
those accidents that involved bodily injury, 40% were partly caused by weather conditions.
I. What is the probability that a randomly chosen accident both was partly caused by
weather conditions and involved bodily injury?
II. Are the events “partly caused by weather conditions” and “involved bodily injury”
independent?
III. If a randomly chosen accident was partly caused by weather conditions, what is the
probability that it involved bodily injury?
IV. What is the probability that a randomly chosen accident both was not partly caused by
weather conditions and did not involve bodily injury?

02) a) A department store manager has monitored the number of complaints received per week
about poor service. The probabilities for numbers of complaints in a week, established by this
review, are shown in the following table.
Number of
complaints
0 1 to 3 4 to 6 7 to 9 10 to 12 More
than 12
Probability 0.14 0.39 0.23 0.15 0.06 0.03
Let A be the event “there will be at least one complaint in a week” and B the event “there will be
fewer than ten complaints in a week.”
I. Find the probability of event A.
II. Find the probability of event B.
III. Find the probability of the complement of event A.
IV. Find the probability of the intersection of events A and B.
V. Are A and B mutually exclusive?