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In each of the following cases, find an interval that contains approximately 95.44 percent of all the possible sample proportions.
If you add 3/5 of a number to the number itself, you get -32. What is the number?
A student is appearing in a multiple-choice exam in which each question has four choices. Assuming that she has no knowledge of the correct answers to any of the questions, she has decided on a strategy in which she will place four balls (marked A, B, C and D) into a box. The marking on the ball will determine her answer to the question. She randomly selects one ball for each question and replaces the ball in the box. There are five multiple-choice questions on the exam.
vi) Find sample space of the correct answers.
vii) If X represents the numbers of correct answers, then find the probability distribution of X.
viii) Find the distribution function of the random variable X and draw its graph.
ix) What is the probability that she will get more than four questions correct?
x) What is the probability that she will get no more than two questions correct?
xi) If each question is of 2 marks, what is the expected value of the correct answers?
Suppose you are working for a company in the music business. They make stereos, musical instruments and produce CD’s. They decide to do a survey on dance preferences by college students. Basically, they wanted to know about college students’ interests and practices on dance music. A survey was administered to a random sample of 37 students and recorded in Table 1:
A – Ironic dance B – Pro dance C – Sway dance
D – Dad-dance E – Twerk dance




Male Female Male Female Male
A A A A E
C E C C A
A A C B E
A C A D D
A A B A A
C D E B B
D A D D A
D A
Based on Table 1 in Question 1:
a) Prepare a multiple frequency table for dance preferences of both genders.
b) Using your frequency table, draw a multiple bar chart to represent the information.
c) Briefly discuss and compare the percentage of favorite and least favorite dance preferences of both genders.
In a project involving skinfold thickness measurements is three groups, a Levene statistic was reported at 3.286 with a significance of 0.68. Is the assumption of homogeneity of variance met for this ANOVA?
1.yes
2. No
3.cant tell
1. Suppose X and Y are independent continuous random variables. Show that
E[X|Y = y] = E[X] for all y

2. The joint density of X and Y is
f (x, y) = (y^2 − x^ 2) * e^(−y), 0 < y < ∞, −y <= x <= y
Show that E[X|Y = y] = 0.
minimum credit hours taken by an it student per semester is normal with mean of 12 credit hours and standard deviation of 3.5 credit hours. the registrar office wishes to establish a credit hours value c beyond which there will be penalty charge. what value of c is such that 99% of all students are at least 1 credit hour under the penalty charge?
Let X={a,b,c,d}, A={ } be a subset of X, T={ ϕ,{a},{a,b},{a,b},X} be a topology on X. Find limit points
Based on Table 1 in Question 1:
a) Prepare a multiple frequency table for dance preferences of both genders.
b) Using your frequency table, draw a multiple bar chart to represent the information.
c) Briefly discuss and compare the percentage of favorite and least favorite dance preferences of both genders.
if H and G are two isomorphic groups then prove that Atu(H) is isomorphic to Atu(G).
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