In the popular American game of roulette, the roulette wheel has
38 spaces that are numbered 0, 00, and 1 through 36, 0.
Find the probability of getting the following:
a) A number that is less than 15, not counting 0 and 00;
b) A number that is a multiple of 3 or 5, not counting 0 and
00;
c) An odd number that is less than 15, not counting 0 and 00;
d) A number that is between 1 and 12, inclusive.
In: Statistics and Probability
A basketball player’s free-throw average is calculated as the average number of made shots relative to total attempts. Suppose Shaquille currently has a 25% free-throw average and is a very consistent (if not a very good) shooter. During today’s game, this player will be at shoot exactly nine free throws (a) What is the probability that he ends up with three made shots? (b) What is the probability he ends up with no made shots? (c) What is the probability he ends up with at least four made shots? (d) What is the probability he ends up with fewer than three made shots?
In: Economics
A baseball player has a .300 batting average; (he gets a hit in 30% of his total “at-bats” (opportunities)). In a particular week, he will have a total of 20 at-bats. Assume that two outcomes are possible at each at-bat, a hit or an “out”. Also, assume that the probability of a hit is constant and that the at-bats are independent.
a. What is the expected number of hits for the week?
b. What is the probability that he gets more than six hits (hits > 6)?
c. What is the probability that he gets five, six, or seven hits.
d. What is the probability that he gets exactly six hits (hits = 6)?
*** Show your work please ***
In: Statistics and Probability
It is estimated that 13% of those taking the quantitative methods portion of the certified public accountant (CPA) examination fail that section. Seventy seven students are taking the examination this Saturday. a-1. How many would you expect to fail? (Round the final answer to 2 decimal places.) Number of students a-2. What is the standard deviation? (Round the final answer to 2 decimal places.) Standard deviation b. What is the probability that exactly six students will fail? (Round the final answer to 4 decimal places.) Probability c. What is the probability at least six students will fail? (Round the final answer to 4 decimal places.) Probability
In: Statistics and Probability
Assume that the probability that a person is killed by coronavirus in a year is, independently, 1/(200 million). Assume that the TR population is 100 million. (5 poi. for each parts)
a. Compute P(3 or more people will be killed by coronavirus next year) exactly.
b. Approximate the probability that found in (a).
c. Approximate the probability that ONO or more people are killed by coronavirus within the first 3 months of next year.
d. Approximate the probability that in exactly 3 of next 10 years exactly 4 people are killed by coronavirus. e. Find the expected number of years, among the next 5, in which 2 or more people are killed by coronavirus.
In: Statistics and Probability
The number of telephone calls coming into the central switchboard of an office building follows a Poisson process with an average of 4 calls per minute.
a) What is the probability that at least 3 calls will arrive in a given one minute period?
b) What is the probability that at least 20 calls will arrive in a given five minute period?
c) What is the probability that the time from the opening of the switchboard until the first call exceeds 20 seconds?
d) What is the probability that the time from the opening of the switchboard until the 4th call is at most 45 seconds?
e) Find the mean and variance for the waiting time between the opening of the switchboard and the 3rd call.
In: Statistics and Probability
A) If two events A and B are __________, then P(A and B)=P(A)P(B).
complements
independent
simple events
mutually exclusive
B)
The sum of the probabilities of a discrete probability distribution must be _______.
less than or equal to zero
equal to one
between zero and one
greater than one
C) Which of the below is not a requirement for binomial experiment?
The probability of success is fixed for each trial of the experiment.
The trials are mutually exclusive.
For each trial there are two mutually exclusive outcomes.
The experiment is performed a fixed number of times.
D) If p is the probability of success of a binomial experiment, what is the probability of failure?
−p
x/n
n/x
1-p
In: Statistics and Probability
The number of telephone calls coming into the central switchboard of an office building follows a Poisson process with an average of 4 calls per minute.
a) What is the probability that at least 3 calls will arrive in a given one minute period?
b) What is the probability that at least 20 calls will arrive in a given five minute period?
c) What is the probability that the time from the opening of the switchboard until the first call exceeds 20 seconds?
d) What is the probability that the time from the opening of the switchboard until the 4th call is at most 45 seconds?
e) Find the mean and variance for the waiting time between the opening of the switchboard and the 3rd call.
In: Statistics and Probability
It is estimated that 16% of those taking the quantitative methods portion of the certified public accountant (CPA) examination fail that section. Seventy students are taking the examination this Saturday.
a-1. How many would you expect to fail? (Round the final answer to 2 decimal places.)
Number of students
a-2. What is the standard deviation? (Round the final answer to 2 decimal places.)
Standard deviation
b. What is the probability that exactly eight students will fail? (Round the final answer to 4 decimal places.)
Probability
c. What is the probability at least eight students will fail? (Round the final answer to 4 decimal places.)
Probability
In: Statistics and Probability
A frequency distribution is shown below. Complete parts (a) through (e). The number of dogs per household in a small town.
(a) Use the frequency distribution to construct a probability distribution. (b) Find the mean of the probability distribution. (c) Find the variance of the probability distribution. (d) Find the standard deviation of the probability distribution. (e) Using the found values of the mean and the standard deviation, an interpretation of the results in the context of the real-life situation is that a household on average has _ dog with a standard deviation of _ dog.
Dogs x=0 1 2 3 4 5
Households p(x)= 1225 408 164 44 25 15
In: Math