Based on long experience, an airline found that about 2% of the people making reservations on a flight from Miami to Denver do not show up for the flight. Suppose the airline overbooks this flight by selling 267 ticket reservations for an airplane with only 255 seats.
(a) What is the probability that a person holding a reservation
will show up for the flight?
(b) Let n = 267 represent the number of ticket
reservations. Let r represent the number of people with
reservations who show up for the flight. What expression represents
the probability that a seat will be available for everyone who
shows up holding a reservation?
P(r ≤ 255)
(c) Use the normal approximation to the binomial distribution and
part (b) to answer the following question: What is the probability
that a seat will be available for every person who shows up holding
a reservation? (Round your answer to four decimal places.)
In: Statistics and Probability
An individual who has automobile insurance from a certain company is randomly selected. Let Y be the number of moving violations for which the individual was cited during the last 3 years. The pmf of Y is given.
| y | 0 | 1 | 2 | 3 |
|---|---|---|---|---|
|
p(y) |
0.50 | 0.30 | 0.15 | 0.05 |
(a)
What is the probability that among 15 randomly chosen such individuals, at least 10 have no citations? (Round your answer to three decimal places.)
(b)
What is the probability that among 15 randomly chosen such individuals, fewer than half have at least one citation? (Round your answer to three decimal places.)
(c)
What is the probability that among 15 randomly chosen such individuals, the number that have at least one citation is between 5 and 10, inclusive? ("Between a and b, inclusive" is equivalent to
(a ≤ X ≤ b).
Round your answer to three decimal places.)
In: Statistics and Probability
A product with an annual demand of 900 units has Co = $18.50 and Ch = $7. The demand exhibits some variability such that the lead-time demand follows a normal probability distribution with µ = 26 and σ = 6. Note: Use Appendix B to identify the areas for the standard normal distribution.
a) What is the recommended order quantity? Round your answer to the nearest whole number.
b) What are the reorder point and safety stock if the firm desires at most a 5% probability of stock-out on any given order cycle? If required, round your answers to the nearest whole number.
Record point =
Safety stock =
c ) If a manager sets the reorder point at 32, what is the probability of a stock-out on any given order cycle? If required, round your answer to four decimal places. P(Stockout/cycle) =
In: Advanced Math
Elementary statistics – Final assignment – Part two
NOTE : Don’t use p-value for your decision in hypothesis testing
problem
Q2: a) You are interested in the average emergency room (ER)
wait time at your local hospital. You
take a random sample of 50 patients who visit the ER over the past
week. From this sample, the
mean wait time was 30 minutes and the standard deviation was 20
minutes. Find a 95%
confidence interval for the average ER wait time for the hospital.
Interpret your result.
b) An experiment was carried out in which the result can either be
a “positive” reaction or a
“negative” reaction. If the probability of a positive reaction is
0.4 and the experiment is repeated 6
times,
i) what is the probability that the number of positive reactions
will be 2 times
ii) what is the probability that the number of positive reactions
will be At least 1 times
In: Statistics and Probability
In a certain lottery, six numbers are randomly chosen form the set {0, 1, 2, ..., 49} (without replacement). To win the lottery, a player must guess correctly all six numbers but it is not necessary to specify in which order the numbers are selected.
(a) What is the probability of winning the lottery with only one ticket?
(b) Suppose in a given week, 6 million lottery tickets are sold. Suppose further that each player is equally likely to choose any of the possible number combinations and does so independent of the selections of all other players. What is the probability that exactly four players correctly select the winning combination?
(c) Again assuming 6 million tickets sold, what is the most probable number of winning tickets?
(d) Repeat parts (b) and (c) using the Poisson approximation to the binomial probability distribution. Is the Poisson distribution an accurate approximation?
In: Statistics and Probability
Sports and Leisure. The reality television series Splash! features celebrities attempting to learn how to dive. The first episode aired in January 2013 and earned a 23.6% audience share. That is, 23.6% of all TVs in use during the show time period were tuned to a station airing Splash!. 24 people who watched TV during that time period were selected at random.
(a) Find the probability (±0.0001) that at least six watched Splash! P(X⩾6) = .9600
(b) Find (±0.0001) the expected number of people who watched Splash!. μ = 5.664
(c) Find the probability (±0.0001) that the number of people who watched Splash! is less than the mean. P(X<μ) =
(d) Suppose that at most three people watched Splash!What is the probability (±0.0001) that no one watched Splash! ? P(X=0|X⩽3) =
In: Statistics and Probability
According to the CDC, certain microbes are becoming resistant to antibiotic drug therapy and therefore pose a serious public health risk. The CDC lists antibiotic-resistant gonorrhea as one of most serious of these kinds of infections. 30% of all gonorrhea infections are antibiotic-resistant. Suppose that 15 individuals are receiving treatment for gonorrhea at a particular clinic. Use what you know about the binomial distribution to answer the following questions.
a. What is the probability that exactly 5 of the 15 individuals have antibiotic-resistant gonorrhea?
b. What is the probability that 5 or fewer of these individuals have antibiotic-resistant gonorrhea?
c. What is the probability that more than 7 of these individuals have antibiotic-resistant gonorrhea?
d. What is the expected number of individuals that have antibiotic-resistant gonorrhea?
e. What is the standard deviation of the number of individuals that have antibiotic-resistant gonorrhea?
In: Statistics and Probability
A book page contains on average 50 lines and each line contains on average 60 characters. The probability that there is character typo is 0.0001. A line or a page contains a random amount of character typos and we want to use the laws or probability to study them. We designate by X, the random variable related to the number of character typos in a line and Y is the random variable related to the number of character typos in a page.
1) Determine the laws of probability of the random variables X and Y
2) Calculate the probabilities of finding in 1 line- 0 typos, 1 typos, 2 typos, at least 1 typo
3) Calculate the probabilities of finding in 1 page- 0 typos, 1 typos, 2 typos, at least 1 typo
4) Calculate the probabilities of finding 2 typos in a page, and the two typos being on the same line
In: Statistics and Probability
Linda is a sales associate at a large auto dealership. At her commission rate of 25% of gross profit on each vehicle she sells, Linda expects to earn 360 for each car sold and 410 for each truck or SUV sold. Linda motivates herself by using probability estimates of her sales. For a sunny Saturday in April, she estimates her car sales as follows:
| Cars sold | 0 | 1 | 2 | 3 |
| Probability | 0.3 | 0.35 | 0.15 | k |
Linda's estimate of her truck or SUV sales is
|
Truck or SUV sold |
0 | 1 | 2 |
| Probability | 0.4 | 0.45 | 0.15 |
Calculate:
5. Lindas best estimate of her earnings for the day.
6. the variance of the number of cars Linda sells for the day.
7. the variance of the number of trucks or SUVs Linda sells for the day.
8. the variance of Linda's earnings for the day.
In: Statistics and Probability
Recently, a nurse commented that when a patient calls the medical advice line claiming to have the flu, the chance that he or she truly has the flu (and not just a nasty cold) is only about 4%. Of the next 25 patients calling in claiming to have the flu, let ? be the number of patients in the sample that actually have the flu.
Explain why ? can be treated as a binomial random variable.
• Identify ? (the number of trials): ? = ___________
• Specify (in words) which event would be defined as a “success”
• Explain why the trials may be considered independent:
• Give the value of ? (the probability of success): ? = ___________
b) On average, for every 25 patients calling in, how many do you expect to actually have the flu?
c) What is the probability that exactly 5 of the 25 patients actually have the flu?
d) What is the probability that at least two of the 25 patients actually have the flu?
In: Statistics and Probability