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A study of a new cholesterol drug measures the decrease in LDL (the "bad" cholesterol) of a group of 500 of patients. The drop in cholesterol followed an approximately Normal distribution: N(-20.0, 2). What is the probability that a person chosen at random will have a cholesterol drop of between -22 and -18?

22 is z=-1 and -18 is z=+1. The area between -1 and +1 is about 68%.

What is the probability of rolling a number >=4 or is odd?

5/6 P(A OR B) = P(A) + P(B) - P(A and B). ---> P(>=4) = 3/6 {4,5,6}---> P(Odd) = 3/6 {1,3,5}---> P(>=4 and Odd) = 1/6 {5}--->3/6+3/6-1/6 = 5/6

Which of the following best describes empirical probability?

A probability that is derived from data.

What is the best way to ensure that you will accurately identify your sample space?

By reading the question carefully. It is always reasonable to look for bias, use proper terminology, and question where the probabilities were determined

When encountering an 'or' probability question, what are the next steps?

Decide to use the the addition rule, and then determine if the events are disjoint.

When encountering an 'and' probability question, what are the next steps?

Decide to use the the multiplication rule, and then determine if the events are independent.

For this question, define the EVENT space:In playing cards, there are 4 suits: Hearts, Diamonds, Spades, Clubs. Hearts and Diamonds are red. Spades and Clubs are black. If you randomly pick a card from the deck, what is the probability of picking one of the two black suits?

E = {Spades, Clubs}

We notate two events as follows: Event A: Chicago Blackhawks win the championshipEvent B: All players remain healthy True/False:The probability that the Chicago Blackhawks will win the championships if all players remain healthy can be notated as P(B | A)

F False: The statement P(B|A) would read 'The probability that all players remain healthy GIVEN that the Blackhawks win the championship.'

n 15 tosses of a coin, the possible number of heads is shown by the sample space: {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15} True/False: This is a continuous sample space.

F This is a discrete sample space. Even though the sample space seems like there are quite a few numbers, it is still very much finite and each item can be clearly identified.

The two events mentioned here are DISJOINT: - The Chicago Bears (football) win the championship in the year 2030.- The Chicago Blackhawks (hockey) win the championship in the year 2030.

F both can happen

The probability that the Chicago Blackhawks will win the championship and that all players will remain healthy is 0.043. The probability that all players will remain healthy is 0.2. What is the probability that the team will win the championships given that all players remain healthy?

Hide question 10 feedback The key is to clearly identify the events and then to keep track of them. Remember not to interchange P(A|B) and P(B|A) --> these are entirely different statements! Recall the formula: P(B|A) = P(A and B) / P(A)So, if the statement is P(Team Wins | Players are healthy), thenA = Players remain healthyB = Team winsP(B|A) = 0.043/0.2= 0.215

A soccer (or football) teams wins 60% of their games. Express the likelihood of the team losing a game in terms of probability.

P(Lose a game) = 0.4

In a group of 200 flowers, 40 are roses, 10 are lilacs, 10 are red, 6 are blue. 8 flowers are both red and roses. What is the probability of finding a flower that is either red or a rose?

P(Red or Rose) = P(Red) + P(Rose) - P(Red and Rose) = 10/200 + 40/200 - 8/200= 42/200 (0.21)

The expected value of a random variable can only be expected to occur over the average of many, many repetitions of the trial/experiment.

T

The minimum recorded size of a certain species of bacteria is 0.00001 inches. The maximum recorded size is 0.00002 inches. True/False: The sample space for the possible sizes of this bacteria species is continuous.

T

The two events mentioned here are DISJOINT: - Bradd Pitt Jr will win the Oscar for Best Actor in 2030.- George Clooney Jr will win the Oscar for Best Actor in 2030.

T

True/False: If two events, A and B are independent, then we can say that: P(B|A) = P(B)

T If two events are independent, then P(B) will be the same regardless of whether or not event A occurs. So if P(B) is, say, 0.2, then P(B|A) will not be any different, and will also be 0.2.

P(A or B) = P(A) + P(B).What is the proper and best name for this rule?

The Addition Rule for Disjoint Events

What is the expected value of a single roll of the die?

The expected value is simply the mean of a discrete random variable. Take each outcome and multiply it by its probability. Then add them together

A study of a new cholesterol drug measures the decrease in LDL (the "bad" cholesterol) of a group of 5 of patients. The recorded changes in cholesterol were -20.4, -18.0, -7, -2.8, -3.2. What is the expected value of the drop in cholesterol for this drug?

Unable to determine. We would need to examine a density curve. Every possible amount of cholesterol loss or gain can not be explicitly identified. In other words, it is a continuous interval. The only way to determine the mean (expected value) of a continuous interval is by looking at a density curve.

The probability of flipping a coin and getting a heads is 1/2. How was this probability determined?

We know that any particular result on a coin flip has a 1/2 chance of occuring. This is an example of a theoretical probability. We do not need to look at previously recorded data (empirical data) to come up with this probability.

There are 52 cards in a deck. You pick a card from the deck and get the Ace of Hearts. The probability of doing so is 1/52. You then return that card to the deck. You then pick another card at random from the deck. Is the probability of getting the 7 of Diamonds also 1/52?

Yes because these events are independent.

Can the general addition rule be used for disjoint events? If so, why?

Yes it can. It works because when two events are disjoint, the P(A and B) term equals 0.

A couple plans to have 6 children because they want 3 boys and 3 girls. A statistician friend tells them this is not a very good idea as their desired outcome is unlikely. Is their friend correct?

Yes. Random events only approach their expected outcome with consistency over many repititions.

You encounter an 'and' question involving two events are not independent. Which of the following statements would be true?

You are going to need to include a conditional probability in your calculations.

You flip a (fair) coin 10 times and get 10 heads and 0 tails. What result can you expect to get on the next role.

none Coin tosses are independent of one another. The result of any one roll is in no way affected by whatever came previously.

True/False: You can ALSO apply the general multiplication rule to independent events.

t

If you randomly sampled 4000 births in a local hospital, and assuming there is no societal/cultural bias towards boys v.s. girls, you can safely assume to end up with approximately 50% boys and 50% girls.

t with many repititons

Lilacs are usually purple, but are sometimes white. In a group of 200 flowers, 40 are roses, 10 are lilacs, 10 are red, 6 are blue, 7 are purple. 8 are both red and roses. What is the probability of finding a flower that is either purple or a lilac?

unable

A study of a new cholesterol drug measures the decrease in LDL (the "bad" cholesterol) of a group of 500 of patients. The drop in cholesterol followed an approximately Normal distribution: N(-20.0, 2). What is the probability that a person chosen at random will have a cholesterol drop of -20?

unable of a signle value

You roll 5 dice. What is the sample space for the number of 6s you could end up with?

{0, 1, 2, 3, 4, 5}

In a single roll of a die, I am interested in knowing if I will roll an even number. Which of the following is an appropriate EVENT space for this question?

{2, 4, 6} Recall that the sample space lists ALL the possible outcomes. The event space lists ONLY the outcomes that you are looking for.