Events A and B are two non-mutually exclusive events with the following probabilitiesdefined:A.p(An B') = 0. 13,p(AU B)' = 0. 41, p(A'n B) = 0.38(i)Draw a fully labeled Venn diagram showing the probabilities of all the regions inthe sample space.Question 4A (cont’d)(ii)Determine the following probabilities using the addition and conditionalprobability rules:p(A' U B)p(A|B')В.A deck of 10 cards marked 2, B, B, 5, 5,5 8, D, D and F, are to be arranged on thetable.(i)If you were to select 5 cards from the deck, what is the probability that all 5 cardsare numeric cards?(ii)What is the probability of having an arrangement where the B's are in the firstand the last position?A study was conducted to investigate the relationship between a person's hand strengthand its stretchability. A random sample of 20 students was selected and their handstrength and how much they can stretch was measured.Their hand strength values range from 1 – 10 points, while the stretchability valuesrange from 1 mm – 15 mm.C.The results are summarized as follows:Ex = 109, x? = 787, Ey = 143, y² =1575,ху 3D 1036(i)Calculate the correlation coefficient of the two variables. Hence, comment on therelationship between hand strength and stretchability.(ii)Write the equation of the linear regression line of the stretch on the handstrength?(iii) Predict the stretch of a person who has a hand strength of 12. Is this predictionreliable? Explain your answer.

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MATLAB: An Introduction with Applications

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Author:Amos Gilat

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Chapter1: Starting With Matlab

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3.) In an experiment on the behavior of young children, each subject is placed in an area with 5 toys. Past experiments have shown that the probability distribution of the number X of toys played with by a randomly selected subject is as follows. Number of Toys Probability 2 3 4 5 0.03 0.16 0.30 0.23 0.17 a.) Find the P(X = 5). b.) If a subject is chosen at random, what is the probability they played with more than 2 toys? c.) If a subject is chosen at random, what is the probability they played with less than 3 toys? d.) Find the expected number of toys played with. e.) Find the standard deviation of the number of toys played with.
While an independent samples t-test compares two separate groups of people, a paired sample t-test compares the same group of people over time or across two different treatments or events or etc. True False
An experiment can result in one of five equally likely simple events, E₁, E₂, A: E₂, E4 2' P(A) = = 0.4 B: E₁, E3, E4, E5 P(B) = 0.8 C: E₂, E3 Refer to the following probabilities. P(A n B) = 0.2 P(AIB) = 0.25 P(BIA) P(BU C) = 1 P(BIC) 0.5 P(CIB) 0.25 Use the Addition and Multiplication Rules to find the following probabilities. (a) P(AUB) (b) P(An B) = 0.5 P(A U B) = ---Select--- + ---Select--- ✓ P(A n B) = ---Select--- (c) P(B n C) Yes P(B n C) = ---Select--- No P(C) = 0.4 . P(B) = = P(C) = = ---Select--- V = Do the results agree with those obtained by listing the simple events in each? P(A U B) = P({E₁, E₂, E3, E4, E5}) = 1 P(A n B) = P({E₁}) = 0.2 P(B n C) = P({E3}) = 0.2 .., E5. Events A, B, and C are defined as follows.
Suppose that 55% of all adults regularly consume coffee, 45% regularly consume carbonated soda, and 70% regularly consume at least one of these two products. (a) What is the probability that a randomly selected adult regularly consumes both coffee and soda? (b) What is the probability that a randomly selected adult doesn't regularly consume at least one of these two products?
In the country of United States of Heightlandia, the height measurements of ten-year-old children are approximately normally distributed with a mean of 53.3 inches, and standard deviation of 2.2 inches.What is the probability that the height of a randomly chosen child is between 51.3 and 57.1 inches? Do not round until you get your your final answer, and then round to 3 decimal places.Answer=___________ (Round your answer to 3 decimal places.)
The accompanying data are from an article. Each of 309 people who purchased a Honda Civic was classified according to gender and whether the car purchased had a hybrid engine or not. Male Female Hybrid 76 33 Not Hybrid 116 84 Suppose one of these 309 individuals is to be selected at random. Determine if the probabilities P(hybrid male) and P(male hybrid) are equal. If not, explain the difference between these two probabilities. O Yes, the probabilities are equal. No, the probabilities are not equal. The first is the probability that a hybrid Honda Civic owner is male, and the second is the probability that a male Honda Civic owner purchased a hybrid. O No, the probabilities are not equal. The first is the probability that a male Honda Civic owner purchased a hybrid, and the second is the probability that a hybrid Honda Civic owner is male.
2 A random sample of size 12 drawn from a population of size 200. The sample values and their probabilities are (52,0.004), (72,0.003), (64,0.005), (58,0.003), (42,0.002), (76,0.006), (71,0.006), (63,0.006), (87,0.008), (57,0.002), (61,0.003) and (86,0.007). Estimate population total with a 95% confidence interval by using probability proportional to size sampling.

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