Statistics and Probability Answers

The Olive Construction Company is determining whether it should submit a bid for a new shopping center. In the past , Olive’s main competitor , Base Construction Company ,has submitted bids 80% of the time. If Base Construction Company does not bid on a job ,the probability that the Olive Construction Company will get the job is 0.50. If Base Construction Company does bid on a job, the probability that the Olive Construction Company will get the job is 0.25. If the Olive Construction Company will get the job, what is probability that, Base Construction Company did not bid?

In an experimental group of 250 individuals, half were given regular doses of aspirin while the other half were given placebos with no effects. Test the claim that the aspirin group has a significantly lower heart attack rate than the placebo group.

In a typical month, an insurance agent presents life insurance plans to 40 customers. Historically, one in four such customers chooses to buy life insurance from this agent. Based on the relevant information, answer the following questions:
(i) What is the probability that exactly 5 customers will buy life insurance from this agent in the coming month?
(ii) What is the probability that no more than 10 customers will buy life insurance from this agent in the coming month?
(iii) What is the probability that at least 20 customers will buy life insurance from this agent in the coming month?
(iv) Determine the mean and standard deviation of the number of customers who will buy life insurance from this agent in the coming month.

Given the following information of first year students of a particular school.
​​​​​​​
Age (Years)
23
24
26
28
29
Number of students
8




Probability
1.5a
2.5 a
0.4
0.25
0.1
​
Find
i. a
ii. Interquartile range

The probability that a student passing a CAT is ¾, if he pass the CAT, the probability of getting grade A finally is 5/6. If he fails the probability of getting on A would be 1/5. If a student gets a grade A what is the probability that he passed the CAT

3.3.14 Let X and Y be independent, with X ∼ Bernoulli(1/2) and Y ∼ N(0, 1). Let
Z = X +Y and W = X −Y. Compute Var(Z), Var(W), Cov(Z, W), and Corr(Z, W

3.3.13 Let X and Y be independent, with X ∼ Bernoulli(1/2) and Y ∼ Bernoulli(1/3).
Let Z = X + Y and W = X − Y. Compute Cov(Z, W) and Corr(Z, W).

3.3.12 Suppose you flip four fair coins. Let X be the number of heads showing, and
let Y be the number of tails showing. Compute Cov(X, Y) and Corr(X, Y).

Find the percentile rank for 623

804 736 659 489 777 623 597 524 228

3.3.11 Suppose you roll two fair six-sided dice. Let X be the number showing on the
first die, and let Y be the sum of the numbers showing on the two dice. Compute E(X),
E(Y), E(XY), and Cov(X, Y).