In southern California, a growing number of persons pursuing a teaching credential are choosing paid internships over traditional student teaching programs. A group of ten candidates for three teaching positions consisted of seven paid interns and three traditional student teachers. Assume that all tencandidates are equally qualified for the three positions, and that x represents the number of paid interns who are hired.
(a)
Does x have a binomial distribution or a hypergeometric distribution? Support your answer. (Round your answer to four decimal places.)
(b)
Find the probability that three paid interns are hired for these positions. (Round your answer to four decimal places.)
(c)
What is the probability that none of the three hired was a paid intern? (Round your answer to four decimal places.)
(d)
Find
P(x ≤ 1).
In: Statistics and Probability
| Suppose that x has a Poisson distribution with μ = 22. |
| (a) |
Compute the mean, μx, variance, σ2xσx2, and standard deviation, σx. (Do not round your intermediate calculation. Round your final answer to 3 decimal places.) |
| µx = , σx2 = , σx = |
| (b) |
Calculate the intervals [μx ± 2σx] and [μx ± 3σx ]. Find the probability that x will be inside each of these intervals. Hint: When calculating probability, round up the lower interval to next whole number and round down the upper interval to the previous whole number. (Use the value for standard deviation from part a. Round all your answers to 4 decimal places. Negative amounts should be indicated by a minus sign.) |
| [µx ± 2σx] | [ , ] |
| P( ≤x ≤ ) | |
| [µx ± 3σx] | [ , ] |
| P( ≤x ≤ ) |
In: Statistics and Probability
Fast food franchises considering a drive up window food service operation. assume that cars arrive at the service following a position distribution at a rate of 24 customers per hour. assume that the service distribution is exponential arriving customers place orders on an intercom station at the back of the parking lot and then drive to the service window to pick up their orders and pay for the service.
the situation can be implemented using a single server operation for where an employee who fills the order and the one who takes the money from the customer the average service time for this alternative is 1.45 minutes.
operating characteristics
Probability of no cars in the system
average number of cars waiting for service
average number of cars in the system
average time a car waits for service
average time in the system
probability that an arriving car will have to wait
In: Statistics and Probability
The GenPik pharmaceutical company wishes to test their fertility medication on a large sample of families with 8 children. To analyze their results, they have asked you to calculate the expected probabilities of such an event.
(1) Create a probability distribution listing the outcomes and probabilities for the number of girls expected in 8 births (keep in mind that x will go from 0 to 8).
(2) Calculate the mean, standard deviation, and variance of your probability distribution.
(3) Using your calculated values above, determine the cutoff values for the number of girls in 8 births that would be unusually high and unusually low.
(4) If 23% of families with 8 children who took GenPik’s medication have over 6 girls, is it reasonable to conclude that the medication significantly increases a couple’s chance of having girls? Explain.
In: Statistics and Probability
In: Statistics and Probability
Suppose each day (starting on day 1) you buy one lottery ticket with probability 1/2; otherwise, you buy no tickets. A ticket is a winner with probability ? independent of the outcome of all other tickets. Let ?? be the event that on day ? you do not buy a ticket. Let ?? be the event that on day ?, you buy a winning ticket. Let ?? be the event that on day ? you buy a losing ticket.
a. Find the PMF of ?, the number of losing lottery tickets you have purchased in ? days.
b. Let ? be the number of the day on which you buy your ? ?ℎ losing ticket. What is ??(?)? Hint: If you buy your ? ?ℎ losing ticket on day d, how many losing tickets did you have after ? − 1 days?
In: Statistics and Probability
6.31. The exponential distribution can be used to solve Poisson-type problems in which the intervals are not time. The Air Travel Consumer Report published by the U.S. Department of Transportation reported that in a recent year, Virgin America led the nation in fewest occurrences of mishandled baggage, with a mean rate of 0.95 per 1,000 passengers. Assume that mishandled baggage occurrences are Poisson distributed. Using the exponential distribution to analyze this problem, determine the average number of passengers between occurrences. Suppose baggage has just been mishandled.
Book says answers are
.μ = 1052.6
a..5908
b..1899 but how?
In: Statistics and Probability
1a) Let an experiment consist of rolling three standard 6-sided
dice.
i) Compute the expected value of the sum of the rolls.
ii) Compute the variance of the sum of the rolls.
iii) If X represents the maximum value that appears in the two
rolls, what is the expected value of X?
1b) Consider an experiment where a fair die is rolled repeatedly
until the first time a 3 is observed.
i) What is the sample space for this experiment? What is the
probability that the die turns up a 3 after i rolls?
ii) What is the expected number of times we roll the die?
iii) Let E be the event that the first time a 3 turns up is after
an even number of rolls. What set of outcomes belong to this event?
What is the probability that Eoccurs?
In: Math
Please try to type your solution for this question, so I can read it without a problem. I truly appreciate you for typing in advance.
The Question:
An FBI survey shows that about 80% of all property crimes go unsolved. Suppose that in your town 3 such crimes are committed and they are each deemed independent of each other. X is the number of crimes will be solved in your town. Complete the table below for the probability mass function and cumulative probability function of the random variable X using the probabilities listed below.
|
X |
0 |
1 |
2 |
3 |
|
P(x) |
0.512 |
0.008 |
||
|
F(x) |
1 |
In: Math
Melanie is the manager of the Clean Machine car wash and has gathered the following information. Customers arrive at a rate of eight per hour according to a Poisson distribution. The car washer can service an average of ten cars per hour with service times described by an ex- ponential distribution. Melanie is concerned about the number of customers waiting in line. She has asked you to calculate the following system characteristics:
(a) Average system utilization 8/10=0.8= 80%
(b) Average number of customers in the system 8/(10-8)=8/2= 4
(c) Average number of customers waiting in line 8^2/10(10-8)= 64/20= 3.2 customers
2. Melanie realizes that how long the customer must wait is also very important. She is also concerned about customers balking when the waiting line is too long. Using the arrival and service rates in Problem 1, she wants you to calculate the following system characteristics:
(a) The average time a customer spends in the system 1/(10-8)= ½ hours
(b) The average time a customer spends waiting in line0.8/(10-8)= 0.8/2 = 0.4 hours
(c) The probability of having more than three customers in the system 0.8^3 =0.512
(d) The probability of having more than four customers in the system 0.8^4 =0.4096
If Melanie adds an additional server at Clean Machine
car wash, the service rate changes to an average of 16 cars per
hour. The customer arrival rate is 10 cars per hour. Melanie has
asked you to calculate the following system characteristics:
(a) Average system utilization
(b) Average number of customers in the system
(c) Average number of customers waiting in line
Melanie is curious to see the difference in waiting times for customers caused by the additional server added in Problem 3. Calculate the following system characteristics for her :
(a) The average time a customer spends in the system
(b) The average time a customer spends waiting in line
(c) The probability of having more than three customers in the system
(d) The probability of having more than four customers in the system
After Melanie added another car washer at Clean Machine (service rate is an average of 16 customers per hour), business improved. Melanie now estimates that the arrival rate is 12 customers per hour. Given this new information, she wants you to calculate the fol- lowing system characteristics:
(a) Average system utilization
(b) Average number of customers in the system
(c) Average number of customers waiting in line
As usual, Melanie then requested you to calculate sys- tem characteristics concerning customer time spent in the system.
(a) Calculate the average time a customer spends in the system.
(b) Calculate the average time a customer spends waiting in line.
(c) Calculate the probability of having more than four customers in the system.
In: Advanced Math