1.

Analyze the following scenario and complete the following: i.Determine what type of approach should be used to calculate the desired probability: Classical, Empirical, or Subjective. ii.Determine the probability of the desired event, if possible, rounding to 3 significant digits.

A chef at a restaurant receives 85 orders during the course of an evening. He made a mistake with 17 of these orders. Based on this, what is the probability that the chef will make an error on the next order he receives?

i. Approach:

(click to select)ClassicalEmpiricalSubjective

ii. Probability of error on next draw:

Round to 3 significant digits. Enter 0 if Subjective.

2.

912 people phoned customer support for help with their internet connection. Technicians were not able to provide a solution for 380 of customers who had called. If one customer is randomly selected from the number of people that phoned:

a.Calculate the probability that it's a customer that technicians were not able to help, rounded to 3 significant digits as needed.

b.Calculate the probability of the complementary event.

3.

Complete the following table and use it calculate the probabilities given below.

	B	Bc	Total
A	0.434	0.214
Ac
Total	0.525		1

a.P(AcorBc)=()=

b.P(AcorB)=()=

c.P(Ac|Bc)=(|)=

Round to 3 decimal places

d.P(Ac|B)=(|)=

Round to 3 decimal places

e. Are the eventsAandBindependent?

(click to select)YesNo

f. Are the eventsAandBmutually exclusive?

(click to select)YesNo

4.

In a survey that asked 77 people to indicate the reasons why they do not go to the gym, 44 responded that they were too busy, 28 said they felt too tired/lazy to go, and 10 said both.

a.If a participant is randomly selected from the study, determine the probability that he/she does not go to the gym because he/she is too busy or because he/she is too tired/lazy.

P(Busy or Tired/Lazy):

Round to 3 significant digits.

b.If a participant is randomly selected from the study, determine the probability that he/she does not go to the gym for reasons not related to busyness or tiredness/laziness.

P(Other):

Round to 3 significant digits.

5.

A consulting firm offers a market viability study to businesses seeking to expand into a new market. In the past, when a business experienced expansion success in a new market, the survey had revealed favourable conditions 75% of the time, and when a business did not experience expansion success in a new market, the survey had revealed unfavourable conditions 95% of the time. If 60% of the businesses that expanded experienced success, what is the probability that a business will experience success given a favourable market report from the consulting firm?

Round to three decimal places if applicable

6.

At the end of a particular season, the data analyst of a hockey team provided the general manager with the following probability distribution ofX,,the team's goal differential (goals forminusgoals against) per game that season.

x	-3	-2	-1	1	2	3	4	5
P(x)()	0.02	0.13	0.26	0.29	0.16	0.07	0.04	0.03

Determine the following probabilities:

a.P(X<0)=(<0)=

b.P(X3)=(3)=

c.P(2

d.P(3

e.P(X<7)=(<7)=

7.

Calculate the mean and standard deviation of the discrete probability distribution.

x	0	5	10	15	20	25	30
P(x)()	0.16	0.05	0.18	0.11	0.23	0.12	0.15

Mean:

Round to two decimal places if necessary

Standard Deviation:

Round to two decimal places if necessary

8.

Analyze the scenario and complete the following:

1. Complete the discrete probability distribution for the given variable.
2. Calculate the expected value and variance of the discrete probability distribution.

The value of a ticket in a lottery, in which 2,000 tickets are sold, with 1 grand prize of $4,500, 5 first prizes of $250, 15 second prizes of $125, and 50 third prizes of $50.

i.

x	0	50	125	250	4,500
P(x)()

Round probabilities to 4 decimal places

ii.

E(X)()=

Round to 2 decimal places

Var(X)()=

Round to 2 decimal places

9.

AssumeXhas a binomial distribution. Use the binomial formula, tables, or technology to calculate the probability of the indicated event:

a.n=21,p=0.6=21,=0.6

P(12X15)=(1215)=

Round to four decimal places if necessary

b.n=19,p=0.7=19,=0.7

P(12

Round to four decimal places if necessary

10.

A certain soda company, "Pop's Soda", claims that 70% of soda drinkers prefer their soda over the other major brands of soda. If this is true, what is the probability that, in a blind taste test involving 20 randomly selected soda drinkers, exactly 70% of those sampled will say they prefer "Pop's Soda" over the other brands of soda tasted?

Round to four decimal places if necessary

11.

In a particular retail clothing store, approximately 20% of potential customers who walk into the store make a purchase. In a random sample of 25 customers that walked into the store,

a.what is the probability that exactly 11 of the customers make purchases?

Round to 3 significant digits.

b.what is the probability that at least 2 of the customers make purchases?

Round to 3 significant digits.

c.how many of the customers are expected to make purchases?

Round to 3 significant digits.

d.what is the standard deviation of the number of customers who make purchases?

Round to 3 significant digits.

12.

A Poisson distribution with=7.4=7.4andx=5=5. Use the probability distribution identified above to calculate the following:

a.The probability P(x) for the indicated value of x. P(5)=(5)=

Round to 3 significant digits

b.The mean and standard deviation of the distribution. Mean ()=Mean ()=

SD ()=SD ()=

Round to 3 significant digits

13.

A bank manager sees an average of 5.5 new clients in her office every day. If the clients arrive at random throughout the day, determine the probability that she will see 4 clients in her office in the first half of the day today. Analyze the given scenario and complete the following:

a.Determine which probability distribution should be used to model the scenario.

Hypergeometric

Geometric

Poisson

b.Calculate the probability of the indicated event. P(x)=()=

Round to 3 significant digits

c.Determine the expected value and variance of the random variable. E(X)=()=

Variance==

Round to 3 significant digits

I need the correct answers.