A doctor wants to estimate the HDL cholesterol of all 20- to 29-year-old females. How many subjects are needed to estimate the HDL cholesterol within 2 points with 99 % confidence assuming sigma equals 14.2 question mark Suppose the doctor would be content with 90 % confidence. How does the decrease in confidence affect the sample size required? A 99% confidence level requires nothing subjects. (Round up to the nearest whole number as needed.) A 90 % confidence level requires nothing subjects. (Round up to the nearest whole number as needed.) How does the decrease in confidence affect the sample size required?
Find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine if the events are unusual. If convenient, use the appropriate probability table or technology to find the probabilities.
The mean number of heart transplants performed per day in a country is about
sevenseven.
Find the probability that the number of heart transplants performed on any given day is (a) exactly
fivefive ,
(b) at least
eighteight ,
and (c) no more than
threethree.
(a)
P(55 )equals=nothing
(Round to three decimal places as needed.)
(b) P(at least
88 )equals=nothing
(Round to three decimal places as needed.)
(c) P(no more than
33 )equals=nothing
(Round to three decimal places as needed.)
Which of the events are unusual? Select all that apply.
A.
The event in part (a) is unusual.
B.
The event in part (b) is unusual.
C.
The event in part (c) is unusual.
Complete parts (a) and (b) using the probability distribution below.
The number of overtime hours worked in one week per employee
|
Overtime hours |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
|
|
Probability |
0.0260.026 |
0.0780.078 |
0.1510.151 |
0.2860.286 |
0.2290.229 |
0.1410.141 |
0.0890.089 (a) Find the mean, variance, and standard deviation of the probability distribution. Find the mean of the probability distribution. muμequals=nothing (Round to one decimal place as needed.) Find the variance of the probability distribution. sigma squaredσ2equals=nothing (Round to one decimal place as needed.) Find the standard deviation of the probability distribution. sigmaσequals=nothing (Round to one decimal place as needed.) (b) Interpret the results in the context of the real-life situation. A. An employee works an average of 1.41.4 overtime hours per week with a standard deviation of approximately 3.43.4 hours. B. An employee works an average of 2.12.1 overtime hours per week with a standard deviation of approximately 1.41.4 hours. C. An employee works an average 3.43.4 of overtime hours per week with a standard deviation of approximately 55 hours. D. An employee works an average of 3.43.4 overtime hours per week with a standard deviation of approximately 1.41.4 hours. |
In: Statistics and Probability
A deck of 11 cards contains 4 red and 7 green cards. Shuffle this deck, then deal 5 cards to Alice and 6 cards to Bob (without any replacement, of course). Let X be the number of red cards that Alice gets, and Y the number of red cards that Bob gets. (a) Write down the joint probability mass function of X and Y . (Write a formula rather than a table.) (b) Are X and Y independent? (c) Compute the conditional probability P(X = 1|Y = 1). Give the result as a decimal.
In: Statistics and Probability
Twelve reindeer at the Bronx zoo during a winter Christmas festival are diagnosed with West Nile Virus. The veterinarian believes the mortality rate for reindeer infected with West Nile Virus is 30% if the disease is left untreated, but can be reduced under treatment to 20%.
a. What is the expected value for the number of reindeer that survive without treatment?
b. What is the expected value for the number of reindeer that survive with treatment?
c. What is the probability less than 5 reindeer survive without treatment?
d. What is the probability less than 5 reindeer survive with treatment?
In: Statistics and Probability
According to a Gallup Poll, 18% of Americans surveyed said that they had gained “a lot” of weight in the past five years. Assume that this result is true for the current population of Americans. A random sample of 14 Americans is selected.
a.Find the probability that in a random sample of 14 Americans, the number who will say they have gained “a lot” of weight in the past five years is at most 2. Draw a distribution
b. Find the probability that in a random sample of 14 Americans, the number who will say they have gained “a lot” ofweights in the past five year is greater than3. Draw a distribution
In: Statistics and Probability
There is a box of 20 marbles. Of these marbles, 6 are red, 8 are green and 6 are blue. 6 marbles are randomly selected from the box without replacement. Let X be the number of marbles that are red or blue, and let Y be the number of marbles that are blue.
1. What is the probability the first and second marbles are red, the third and fourth are blue and the fifth and sixth are green?
2. What is the probability we obtain 2 red, 2 blue and 2 green?
3. Find E (X).
4. Find Var(Y).
5. Find P (X = Y )
In: Statistics and Probability
One red (6 sided) and one white (6 sided) dice is rolled. The random variable X has the value 1 if the red dice shows a number max 2 and is 2 else. The random variable y has the value 1 if the white dice shows a uneven number and is 2 else.
A) determine the common probability function (x,
y)
B) determine the marginal probability functions of x and y
C) calculate e(x), e(x^2), var(x), e(y), e(y^2), and var(y)
In: Statistics and Probability
A bar can have only six barstools. Customers interested in having a drink at this bar arrive at a rate of 6 per hour following a Poisson distribution. It is expected that a customer stays 30 minutes, exponentially distributed. There are only 3 spaces available for customers to wait for a barstool to become available. Customers who want to come in and find there is no room to wait, go to the restaurant next door. Determine:
a. Probability that there are no customers at the bar.
b. The probability that an arriving customer has to wait for a barstool.
c. The average number of customers at the bar.
d. The average number of customers waiting.
In: Statistics and Probability
3. Fun size M&Ms candies contain between 15 and 18 candies and uniformly distributed among bags. Sup- pose a sample of 30 bags is chosen from a large Costco size bag of Fun Size M&Ms.
a) What is the population mean and standard deviation? Hint: bag size is given to us as uniformly distributed
b) What is the probability that the mean number of candies in 30 bags is less than 15 candies?
c) What is the probability that the mean number of candies in 30 bags is more than 18 candies?
In: Statistics and Probability
Suppose there is a basket containing one apple and two oranges. A student randomly pick one fruit from the basket until the first time the apple is picked. (Sampling with replacement)
(a) What is the sample space for this experiment? What is the probability that the student pick the apple after i tosses?
(b) What is the expected number of times the students need to pick the apple?
(c) Let E be the event that the first time an apple is picked up is after an even number of picks. What set of outcomes belong to this event? What is the probability that E occurs?
In: Math
A toll-free phone number is available from 9 a.m. to 9 p.m. for your customers to register complaints about a product purchased from your company. Past history indicates that an average of 1.0 calls are received per minute. Complete parts (a)through (c).
A. what is the probability that during a 1 min period zero phone calls will be received?
B. what is the probability that during a 1 min period three or more phone calls will be received?
C. what is the maximum number of phone calls that will be received in a 1 min period 99.99% of the time?
In: Math