Q1)find the area between z=-2

Q1)find the area between z=-2.48 and z=-.83

Q2

In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities. Do you try to pad an insurance claim to cover your deductible? About 40% of all U.S. adults will try to pad their insurance claims! Suppose that you are the director of an insurance adjustment office. Your office has just received 134 insurance claims to be processed in the next few days. Find the following probabilities. (Round your answers to four decimal places.)

(a) half or more of the claims have been padded

(b) fewer than 45 of the claims have been padded

(c) from 40 to 64 of the claims have been padded

(d) more than 80 of the claims have not been padded

Q3

On hot, sunny, summer days, Jane rents inner tubes by the river that runs through her town. Based on her past experience, she has assigned the following probability distribution to the number of tubes she will rent on a randomly selected day. x 25 50 75 100 Total P(x) .20 .40 .30 .10 1.00 (a) Find the probability expressions. (Round your answers to 2 decimal places.) a. P(X = 75) b. P(X ≤ 75) c. P(X > 50) d. P(X < 100) (b) Which of the probability expressions in parts (a)–(d) is a value of the CDF? Part (a) Part (b) Part (c) Part (d)

Q4

 a bag contains 4 red marbles and 6 blue marbles. A marble is drawn and then replaced. This is done 50 times. What is the exact probability that a red marble is drawn

Q5

Let X1, X2,... be independent, identically distributed random variables with E[X] = 2 and var(X)=9, and let Yi = Xi/2i . We also define Tn and An to be the sum and the sample mean, respectively, of the random variables Y1,...,Yn.

(a) Evaluate the mean and variance of Yn, Tn, and An.

(b) Does Yn converge in probability? If so, to what value?

(c) Does Tn converge in probability? If so, to what value?

(d) Does An converge in probability? If so, to what value?