An urn contains 9 red marbles, 7 white marbles, and 5 blue marbles marbles. A child randomly selects three (without replacement) from the urn. Round to four decimal places. a. Find the probability all three marbles are the same color. b. Find the probability that none of the three marbles are white.

Consider the following data: Step 1. Find the expected value E(X). Round your answer to one decimal place. Step 2. Find the variance. Round your answer to one decimal place. Step 3. Find the standard deviation. Round your answer to one decimal place. Step 4. Find the value of P(X39). Round your answer to one decimal place. Step 5. Find the value of P X £ 7]. Round your answer to one decimal place.

Suppose the mean income of firms in the industry for a year is 80 million dollars with a standard deviation of 3 million dollars. If incomes for the industry are distributed normally, what is the probability that a randomly selected firm will earn between 83 and 85 million dollars? (Round your answer to 4 decimal places)

A zero coupon bond with a face value of $1,000 is issued with an initial price of $430.84 based on semiannual compounding.The bond matures in 20 years. What is the implicit interest, in dollars, for the first year of the bond's life? . $19.08 b. $25.25 E, $21.47 $18.53 e. $22.56

1. In any one-minute interval, the number of requests for a popular Web page is a Poisson random variable with expected value 300 requests. If the number of requests in a one minute interval is greater than n, where n is the capacity of the Web server, the server is overloaded. Use the central limit theorem to estimate the smallest value of n for which the probability of overload is less than 0.05.

2. Consider the following gamblers ruin problem. A gambler bets $1 on each play of a game.Each time, he has a probability p of winning and probability q = 1-p of losing the dollar bet. He will continue to play until he goes broke or nets a fortune of T dollars. Let X,denote the number of dollars possessed by the gambler after the n-th play of the game.Then X_{n+1}=\left\{\begin{array}{l} X_{n}+1 \text { with probability } p \\ X_{n}-1 \text { with pro ability } 1-p \end{array} \quad \text { for } 0<X_{n}<T\right. X_{n+1}=X_{n}, \text { for } X_{n}=\text { or } X_{n}=T Defined in such a way X, is a Markov chain. The gambler starts with Xo dollars, where0 <Xo < T. (a) Construct the (one-step) transition matrix (b) Let T = 3 and p = 0.55. Find the probabilities of winning T dollars when the initial capital of the gambler is 1,..,T – 1 dollars.

The amount of time a bank teller spends with each customer has a population mean of 3.10 minutes and a standard deviation of 0.40 minute. If you select a random sample of 16 customers, 1. What is the probability that the mean time spent per customer is at most 3minutes? 2. There is an 80% chance that the sample mean is less than how many minutes? 3. What assumption must you make in order to solve (Task 1) and (Task 2)? 4. If you select a random sample of 60 customers, there is an 95% chance that the sample mean is less than how many minutes?

The state education commission wants to estimate the fraction of tenth grade students that have reading skills at or below theeighth grade level. Step 1. Suppose a sample of 2089 tenth graders is drawn. Of the students sampled, 1734 read above the eighth grade level.Using the data, estimate the proportion of tenth graders reading at or below the eighth grade level. (Write your answer as a fraction or a decimal number rounded to 3 decimal places) Step 2. Suppose a sample of 2089 tenth graders is drawn. Of the students sampled, 1734 read above the eighth grade level.Using the data, construct the 98% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level. (Round your answers to 3 decimal places)

Researchers often mark wildlife in order to identify particular individuals across time or space.A study of butterfly migration is designed to determine which location on the butterflies' wingsis best for marking. The six possible locations are those shown as A through F in the figure below. The butterfly in the figure is a monarch (Danaus plexippus). Because marks in certain locations may be more likely to attract predators or cause problems than marks in other locations, the goal is to determine whether the six marking locations result in equivalent chances of successful migration. To test this, researchers plan to mark 3,600butterflies and release them, then count how many arrive displaying each marking location at the end of the migratory path. 20. **What type of butterfly is represented in the figure? 21. How many butterflies does the researcher plan to mark and release? 22. **Why do the researchers need to mark butterflies in different locations? B. Describe location D on the butterfly. 4. How is location A different from location D? Why do researchers mark wildlife? 5. What is the goal of the study?

: Let X be a random variable with cumulative distribution function F. The median of X is the value m for which F(m) = 1/2. Then X < m with probability 1/2 and X > m with probability 1/2. Find m if X is (a) uniformly distributed over the interval [a, b]. (b) normally distributed with parameters u and o. (c) exponentially distributed with parameter A.

In Design and Analysis of Experiments, 6th edition (John Wiley & Sons,2005), D. C. Montgomery describes an experiment that determined the effect of four different types of tips in a hardness tester on the observed hardness of a metal alloy. Four specimens of the alloy were obtained, and each tip was tested once on each specimen, producing the following data Fill the gap in the table. Give all of your answers to 3 significant figures.Analysis of Variance for Hardness The standard deviation for the normal distribution will be%3D