what is the probability that at least two people have the same birthday?

Q: In a large casino, the house wins on one of its games with a probability of 51%. 1:1, meaning that…

A: NOTE-AS PER POLICY I HAVE CALCULATED FIRST MAIN QUESTION ONLY.

Q: When a new machine is not functioning properly, 20% of the items produced are defective. If a random…

A: Let us denote X= number of defective itemsn=sample size=5p=probability of success=20%=0.20X follows…

Q: How many people need to attend a party for there to be a > 80% probability that at least two of them…

A: Given information: The probability that at least two of the people share the same birthday is 0.8.

Q: 2. Willow Brook National Bank operates a drive-up teller window that allows customers to complete…

A: Given that the service times for the drive -up teller follow an exponential probability distribution…

Q: In a popular shopping centre, the waiting time for an ABSA ATM machine is found to be uniformly…

A: The PDF is given by f(x)=1b-a , here a=1,b=5 so it follows: f(x)=15-1=14,1≤x≤50otherwise

Q: 2. The flight time for an airplane traveling from Muscat to Dubai is uniformly distributed between…

A: (a)  Since uniform distribution is a continuous uniform distribution, and there exist infinite…

Q: A sign on the pumps at a gas station encourages customers to have their oil checked, and claims that…

A: Let X be the number of cars needs to have oil added. Given: n=84 and p=1/5=0.2 Hence, X ~ B (n=84,…

Q: 4) According to a recent study, 1 in every 8 women has been a victim of domestic abuse at some point…

A: Given, no of women= 25 1 in every 8 women is abused, therefore p=1/8 = 0.125 Let X be the random…

Q: Suppose that in the bookkeeping operation of a large corporation the probability of a recording…

A: Givenp=0.005n=1000Let "x" be the billings contain a…

Q: Thirty percent of the people called agree to participate in a brief telephone survey. In a random…

A: Let X be a random variable follows Binomial Distribution then pmf of X is  P(x)=nCr px (1-p)n-x ,…

Q: Do Generation X and Boomers differ in how they use credit​ cards? A sample of 1,000 Generation X and…

A: A sample of 1,000 Generation X and 1,000 Boomers revealed the results in the given table.

Q: If we roll an ordinary, six-sided die eight times in a row, what is the probability that at least…

A: Given: Number of times the die rolled is, n=8. The objective is to find the probability of at…

Q: nt consists of recording the sex composition, in order of their births, of a four-child family in…

A: Assuming that a boy is equally likely as a girl to be born into a family,i.e., P(B) = 0.50 and P(G)…

Q: Two unfair coins, both favoring heads, are tossed simultaneously for many trials, with the results…

A: It is given that Number of times two head occurs = 63 Number of times one head and one tail occurs =…

Q: For short distance flights, AVX airways provides three different choices on its snack menu—mixed…

A:

Q: Delta Airlines quotes a flight time of 2 hours, 5 minutes for its flights from Cincinnati to Tampa.…

A: Solution

Q: An experiment consists of recording the sex composition, in order of their births, of a four-child…

A: Given data: The four-child family in which the children were born at different times.   The…

Q: A coin is flipped three times. If heads appears exaclty once, what is the probability that it…

A: The possible outcomes when a coin is flipped three times is,

Q: In a city, 28% of new cars were stolen within one year of purchase. Suppose two new cars were…

A:

Q: 24% of all students enjoy the school lunch.  If there are 2000 students at the school, what is the…

A: It is given that n=2000 and p=0.24.

Q: A particular library has 58 visitors. When the visitors were asked how many books they read that…

A: Solution: From the given information, 20 visitors said they read one book, 22 said they read three…

Q: In a gambling game, a woman is paid $3 if she draws a jack or a queen and $5 if she draws a king or…

A: Given problem   Given that

Q: first- and second-born children of two-children families by gender is shown below. What is the…

A:

Q: The Nationwide Motel Company has determined that 70% of all calls for motel reservations request…

A:

Q: It is known that the defect rate of an iPhone 3%. What is the probability that a batch of 100…

A: Has to find P( no defective ) = ? what is A intersection S

Q: At a certain umiversity, 4% of men are over six feet tall and 1% of women are over 6 fee tall.…

A: Given P(A l B) =0.01 P(B) =0.6 P(A l B') =0.04

Q: In the experiment of flipping a coin four times, what is the probability of obtaining odd number of…

A: Let A and B be two events with P(A) > 0. Then the conditional probability of B given A, denoted…

Q: In a certain congressional district, it is known that 20% of the registered voters classify…

A:

Q: An instructor who taught two sections of engineering statistics last term, the first with 20…

A: From the given information, Consider, X be the discrete random variable. Total (N) =50 Second…

Q: A certain group of women has a 0.63% rate of red/green color blindness. If a woman is randomly…

A:

Q: ong adults in the U.S., 60% choose potatoes as their favorite vegetable.  In an Idaho Potato…

A:

Q: 2. The flight time for an airplane traveling from Muscat to Dubai is uniformly distributed between…

A:

Q: 2. The probabilities that a surgeon operates on 3, 4, 5, 6, or 7 patients in any day are 0.10, 0.20,…

A:

Q: a certain population, a group of people has a 0.23% rate of heterochromia. If a random person is…

A: Probability = number of favorable eventstotal number of events

Q: The Lemon brand cars have a transmission which fails with probability .6, and brakes which fail with…

A: Given info: The Lemon brand cars have a transmission which fails with probability 0.6, and brakes…

Q: In a of the population. It is known that 20 per cent of the males and 5 per cent of the females are…

A: Given : P(Male) = 0.5 P(Female) = 0.5 U = Unemployed , E = Employed P( U | Male) = 0.2 P(U | Female)…

Q: In the St. Petersburg Community College, 30% of the men and 20% of the women are studying…

A: Let M=a student is menW=a student is womenE=a student is studying…

Q: The Merrilee Brokerage House studied two groups of industries (computers and petroleum) and rated…

A: From the table we see that n(computer and low risk)= 10  n(low risk)=10+15=25

Q: Do Generation X and Boomers differ in how they use credit cards? A sample of 1,000 Generation X and…

A:

Q: In responding to a survey question on a sensitive topic (Have you ever tried marijuana? Have you…

A: Suppose 80% of population have not yet tried marijuana and all of those individuals will truthfully…

Q: In a class of 27 learners, what is the probability that at least two learners share the sam…

A:

Q: A particular telephone number is used to receive both voice calls and fax messages. Suppose that 20%…

A: From the provided information, 20% of the incoming calls involve fax messages that is p = 0.2 Sample…

Q: In a certain shipment of 1000 laptops, 20 are defective. If a customer purchases the first 4 laptops…

A:

Q: A researcher wishes to conduct a study of the color preferences of new car buyers. Suppose that 50 %…

A:

Q: An arcraft seam requires 25 rivets. the seam will have to be reworked if any of these rivets is…

A: To work out the required probabilities

Q: In a certain city, the distribution of the first- and second-born children of two-children families…

A:

Q: An aircraft seam requires 25 rivets. The seam will have to be reworked ifany of these rivets is…

A: Given

Q: An experiment consists of flipping a weighted coin with Pr[H]=0.8Pr[H]=0.8. The experiment ends when…

A: It is given that the probability of getting a head is 0.8. The coin is flipped at most two times.…

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!