STAT MODULE 3 EXAM

suppose a life insurance company sells a $280,000 one year life insurance policy to a 19 yo female for $180. The probability that year is 0.999652. Compute and interpret the expected value of this policy to the insurance company.

$82.56...... The insurance company expects to make an average profit of $82.56 on every 19 yo female it insures for one year.

What is the probability of an event that is impossible?

0

Suppose that a probability is approximated to be zero based on the empirical rules. Does this mean the event is impossible?

no

Why would something NOT be a probability model?

Because at least one probability is less than 0

E: a person having an at fault accident F: The same person being prone to road rage

E and F are dependent because being prone to road rage can affect the probability of a person having an at fault accident

A probability experiment is conducted in which the sample space of the experiment is S ={1,2,3,4,5,6,7,8,9,10,11,12}, event E={2,3,4,5,6,7,8,9} and event G= {9,10,11} assume that each outcome is equally likely. List the outcomes in E and G. Are E and G mutually exclusive?

E and G= {9} No

E:a randomly selected person finding cheese revolting F: another randomly selected person finding cheese delicious

E cannot affect F and vice versa because the people were randomly selected, so the events are independent

Describe the sample space of the possible outcomes: Determining a persons' grade: f, so, j, se and gender: m, f

FM, FF, SoM, SoF, JM, JF, SeM, Se,F

T or F: When two events are disjoint, they are also independent

False

If E and F are not disjoint events, then P(E or F) =

If E and F are not disjoint events, then P(E or F)=P(E)+P(F)-P(E and F)

If E and F are disjoint events the P(E or F) =

P(E)+P(F)

Assume the probability of the random variable will be approximated using the normal distribution. Describe the area under the normal curve that will be computed. Find the probability that more than 57 households have a gas stove.

The area to the right of 57.5

In a certain card game, the probability that a player is dealt a particular hand is 0.29. Explain what this probability means. If you play this card game 100 times, will you be dealt this hand exactly 29 times? why or why not?

The probability 0.29 means that approximately 29 out of every 100 dealt hands will be that particular hand. No, you will not be dealt this hand exactly 29 times since probability refers to what is expected in the long term not the short term.

The notation P(F I E) means

The probability of event F given event E

T or F in a probability model, the sum of the probabilities of all outcomes must equal 1

True

T or F, Probability is a measure of the likelihood of a random phenomenon or chance behavior

True

T or F: In a probability model, the sum of probabilities of all outcomes must equal 1.

True

Does this represent a binomial experiment?- an investor randomly purchases 13 stocks listed on a stock exchange. historically, the probability that a stock listed on this exchange will increase in value over the course of a year is 48%. The number of stocks that increase in value is recorded.

Yes, because the experiment satisfies all the criteria for a binomial experiment

what is a random variable?

a numerical measure of the outcome of a probability experiment

a binomial experiment is performed a fixed number of times. what is each repetition of the experiment called?

a trial

A gene is composed of two alleles. An allele can be either dominant or recessive. suppose that a husband and a wife who are both carriers of the sickle-cell anemia allele but do not have the disease, decide to have a child. because both parents are carriers of the disease, each one has a dominant normal cell allele (S), and one recessive sickle-cell allele (s). Therefore the genotype of each parent is Ss. Each parent contributes one allele to his or her offspring with each allele being equally likely. a.List the possible genotypes of their offspring. b. what is the probability that the offspring will have sickle cell- genotype ss? c. what is the probability that the offspring will not have sickle cell but still be a carrier (one normal cell allele and one sickle cell allele)

a. SS, ss, Ss, sS b. 1/4- there is a 25% chance that a randomly selected offspring will have sickle cell anemia c. the probability is 1/2- there is a 50% chance that a randomly selected offspring will be a carrier

The word OR in probability implies that we should use the ___ rule

addition

discrete or continuous? the amount of rain in City B during April

continuous, the possible values are r>or equal to 0

discrete or continuous- the time it takes to fly from City A to City b

continuous-the possible values are t>0

discrete or continuous? the number of customers arriving at a bank between noon and 1 pm

discrete, the possible values are x=0,1,2...

discrete or continuous? the number of points scored during a basketball game

discrete, the possible values are x=0,1,2.....

Discrete or continuous?- the number of lightbulbs that burn out in the next week in a room with 15 bulbs

discrete- the possible values are: x=0,1,2,....15

In a probability a(n) ___ is any process that can be repeated in which results are uncertain

experiment

Two events E and F are ___if the occurrence of event E in a probability experiment does not affect the probability in event F.

independent

In a certain card game, the probability that a player is dealt a particular hand is 0.49. Explain what this probability means. If you play this card game 100 times, will you be dealt this hand exactly 49 times?

means that approximately 49 of every 100 dealt hands will be that particular hand. No you will not be dealt that hand exactly 49 times since the probability refers to what is expected in the long term not short term

The word and in probability implies that we use the ___ rule

multiplication

determine whether the following probability experiment represents a binomial experiment and explain your reasoning-three cards are selected from a standard 52 card deck without replacement. the number of hearts selected in recorded.

no, because the trials of the experiment are not independent and the probability of success differs from trial to trial

seven cards are selected from a standard 52 card deck without replacement. the number of clubs selected is recorded. does the probability experiment represent a binomial experiment?

no, because the trials of the experiment are not independent and the probability of success differs from trial to trial

Find the probability that there is exactly 10 defective parts in a shipment

the area between 9.5 and 10.5

The probability that a randomly selected individual in a country earns $75k per year is 8.5%. The probability that a randomly selected individual in the country earns more than $75k per year, given that individual has earned a Bachelor's degree is 8.5% Are the events "earn more than $75k per year" and " Has a bachelors degree" independent?

yes