According to an​ airline, flights on a certain route are on time 85​% of the time. Suppose 8 flights are randomly selected and the number of on time flights is recorded. Use technology to find the probabilities. Use the Tech Help button for further assistance. ​(a) Determine whether this is a binomial experiment. ​(b) Find and interpret the probability that exactly 6 flights are on time. ​(c) Find and interpret the probability that at least 6 flights are on time. ​(d) Find and interpret the probability that fewer than 6 flights are on time. ​(e) Find and interpret the probability that between 5 and 7 ​flights, inclusive, are on time.

According to an​ airline, flights on a certain route are on time 85​% of the time. Suppose 8 flights are randomly selected and the number of on time flights is recorded. Use technology to find the probabilities. Use the Tech Help button for further assistance. ​(a) Determine whether this is a binomial experiment. ​(b) Find and interpret the probability that exactly 6 flights are on time. ​(c) Find and interpret the probability that at least 6 flights are on time. ​(d) Find and interpret the probability that fewer than 6 flights are on time. ​(e) Find and interpret the probability that between 5 and 7 ​flights, inclusive, are on time.

Five males with an​ X-linked genetic disorder have one child each. The random variable x is the number of children among the five who inherit the​ X-linked genetic disorder. Determine whether a probability distribution is given. If a probability distribution is​ given, find its mean and standard deviation. If a probability distribution is not​ given, identify the requirements that are not satisfied. x ​P(x) 0 0.034 1 0.153 2 0.313 3 0.313 4 0.153 5 0.034 Does the table show a probability​ distribution? Select all that apply.

The Department of Engineering at NJIT conducted a study on the average number of trains passing through the Hoboken train station. The study showed that the average is six per hour and that the passing of these trains is approximated by the Poisson distribution. (a) Find the probability that no trains passed through the Hoboken train station between 8am and 9.0am on Tuesday. (b) Find the probability that exactly four trains passed during that time. (c) Find the probability that exactly six trains passed during that time. (d) Find the probability that ten or more trains passed during that time. Please show all work.

A particular telephone number is used to receive both voice calls and fax messages. Suppose that 20% of the incoming calls involve fax messages, and consider a sample of 20 incoming calls. (Round your answers to three decimal places.)

(a) What is the probability that at most 5 of the calls involve a fax message?


(b) What is the probability that exactly 5 of the calls involve a fax message?


(c) What is the probability that at least 5 of the calls involve a fax message?


(d) What is the probability that more than 5 of the calls involve a fax message

On average, typographical errors (typos) occur in a manuscript every 2.7 pages. Suppose that the entire manuscript has 180 pages and the first chapter of manuscript has 12 pages. Answer the following questions.

a) What probability distribution is most appropriate for calculating the probability of a given number of typos? Give the distribution and its parameters.

b) I just found a typo. What is the probability that there will not be another typo over the next 5 pages?

c) Calculate the probability that a randomly selected passage from the manuscript has less than a page in between typos?

The transmitter transmits either an infinite sequence of 0s with a probability 2/3 or 1s with a probability 1/3. Each symbol, regardless of the others and the transmitted sequence is identified by the receiving device with an error with a probability 0.25. i) Given that the first 5 identified symbols are 0s, find the probability P (000000 | 00000) that the sixth received symbol is also zero. b) Find the average value of a random variable equal to the number of the first 1 written by the receiving device (for example, we received 00001...., our RV takes value 5).

(1) Consider the random experiment where three 6-sided dice are rolled and the number that comes up (1, 2, 3, 4, 5 or 6) on each die is observed.

(a) What is the size of the sample space S of this random experiment?

(b) Find the probability of event E1: “All three numbers rolled are the same.”

(c) Find the probability of event E2: “The sum of the three numbers rolled is 5.”

(d) Find the probability of event E3: “At least one 6 is rolled.” (Hint: it may help to first find the probability of the complementary event.)

An athletic footwear company is attempting to estimate the sales that will result from a television advertisement campaign of its new athletic shoe. The contribution to earnings from each pair of shoes sold is $40. Suppose that the probability that a television viewer will watch the advertisement (as opposed to turn his/her attention elsewhere) is 0.40. Furthermore, suppose that 1% of viewers who watch the advertisement on a local television channel will buy a pair of shoes. The company can buy television advertising time in one of the time slots according to Table below:
Television advertising costs and viewers

(a) Suppose that the company decides to buy one minute of advertising time. Which time slot would yield the highest expected contribution to earnings net of costs? What is the total expected contribution to earnings resulting from the advertisement?
(b) Suppose the company decides to buy two one-minute advertisements in different time slots. Which two different time slots should the company purchase to maximize the expected contribution to earnings? What is the total expected contribution to earnings resulting from these two advertisements?