A store assembles some segment data from their clients. The accompanying diagram sums up the age-related data they gathered:

Age Number of Customers

20-30 72

30-40 60

40-50 56

50-60 93

?60?60 53

One client is picked aimlessly for a prize giveaway.

What is the likelihood that the client is in any event 30 yet no more seasoned than 60?

What is the likelihood that the client is either more seasoned than 50 or more youthful than 30?

What is the likelihood that the client is at any rate 50?

Assume that in a specific country, the likelihood of having red hair is 0.20, and the likelihood of having blue eyes is 0.30. The likelihood of having the two qualities is 0.06. The probabilities are appeared in the Venn graph, where ?An is the occasion that an arbitrarily picked occupant of this nation has red hair, and ?B is the occasion that a haphazardly picked occupant has blue eyes.

A not B Both B not A

0.14 0.06 0.24

A=0.20 B= 0.30

Figure the restrictive likelihood of an individual having blue eyes given that the person has red hair, and utilize the worth to decide if having blue eyes and red hair are autonomous.

P(B/A=)

Having red hair is? of having blue eyes in light of the fact that?

i11i

a) Market research has shown that 60% of people who are acquainted with a specific item really purchase the item. An arbitrary example of 15 people were acquainted with the item.

I. Characterize the variable of interest for this situation.

ii. What likelihood circulation do you think best depicts the circumstance? Why?

iii. Compute the likelihood that precisely 9 will purchase the item.

iv. On the off chance that 80 people are acquainted with the item, decide the quantity of individual who are required to purchase the item.

b) It is realized that a normal of 5 trains go through Grand Central Terminal like clockwork. Discover the likelihood that

I. Precisely 4 trains will pass in a short time

ii. under 2 trains will pass in 60 minutes

The Chief Information Officer (CIO) at Old Dominion University - ODU-is attempting to improve the college's data network security. The CIO is attempting to assess another interruption discovery innovation on the lookout for a potential trade for the current framework. An interruption recognition framework sounds an "alert" each time conceivable malevolent assault on an organization is identified. The accompanying data is given:

Occasion of interest, A, is an assault

Proof, B, is interruption recognition framework setting off because of abnormal traffic

Likelihood of an assault is 0.01

For the right now introduced situation, the likelihood of a caution given that there is an assault is 0.9, while the likelihood of an alert given there is no assault is 0.25.

For the new innovation, the likelihood of an alert given that there is an assault is 0.8, while the likelihood of a caution given there is no assault is 0.1.

The CIO expects that there are just two sorts of occasions: either there is, or there is no assault.

The CIO is utilizing "proof proportion," depicted as P(B|A)/P(B|A') as an approach to look at the innovations. Kindly assistance the CIO contrast the new innovation and the as of now introduced framework by addressing the accompanying inquiries:

What is proof proportion for the right now introduced situation?

Using the data below write a discussion paragraph using BOTH descriptive and inferential statistics: Compare the number of years of education for people who have tried marijuana and those who have not. 1. Descriptive Analysis a. Numerical Summaries Table IQR 12.00 13.00 13.29 16.00 23.00 Standard Deviation: N0 =N/A YES = 1689 b. Graphical Summaries Comparing Years of Education and Marijuana Use YES I 0 Marijuana Use NO Years of Education Problem No. 7.3 / 10 pts. Let descrete random variable X ~ Poisson(7). Find: 1) Probability P(X = 8) 2) Probability P(X = 3) 3) Probability P(X 7) 5) HX 6) Ox Show your explanations. Displaying only the final answer is not enough to get credit. Note: round calculated numerical values to the fourth decimal place where applicable. Solution (Show all intermediate steps, formulas, calculations, explanations and comments below this line. Don't write above this line)(51 3x4 = 12 Marks] 10 Let A = {n |1 s n s 12 } and consider a poset (A, R) with the relation R given by the digraph on the right. a) Draw the Hasse diagram for (A, R). b) Find the maximal, minimal, greatest, least 12 elements of (A, R). c) List the upper and lower bounds of the set (5,15]. ( Hint: You may list the relation R explicitly to answer all questions)QUESTION 1: (10 marks) a) By using roster notation, express the set of positive integers less than 25 and greater or equal to 21. b) Check the following statements are TRUE or FALSE, justify your answer. i. 13 5954 7 and 21 are relatively primes. c) Given GCD(12,30) = 6 , Determine LCM(12,30). d) State why Z (the set of all integers) is not a group under multiplications. Define an Abelian group, give one example