Suppose X has an exponential distribution with mean equal to 16. Determine the following: (a) P(X > 10) (Round your answer to 3 decimal places.) (b) P(X > 20) (Round your answer to 3 decimal places.) (c) P(X < 30) (Round your answer to 3 decimal places.)

A farmer in Indiana wants to examine the relation between the number of very hot days (days when the high temperature exceeds 95° F) and the corn production of his farm (in bushels of corn per acre). He looks at the data for 10 summers. Let x¡ = the number of hot days during the ith summer. %3D = the corn production (in bushels per acre) during the ih summer. Let yi The data are in the table below:. 4 6. 7 8. 9. 10 i 2 14 10 7. 8. 1 12 Xi Yi 95 80 83 87 88 85 99 102 79 95 a) Make a scatterplot of the data. b) Examine your scatterplot and, without performing any calculations, EXPLAIN whether you expect the correlation coefficient to be closer to -1, 0, or 1 and WHY. c) Find the sample mean and standard deviation for each variable. %3D %3D S. %3D y d) Place an asterisk on your scatterplot at the point (x,ỹ).

Suppose that fund-raisers at a university call recent graduates to request donations for campus outreach programs. They report the following information for last year's graduates. Size of donation Proportion of calls 0.40 $0 0.30 0.25 Three attempts were made to contact each graduate. A donation of $0 was recorded both for those who were contacted but declined to make a donation and for those who were not reached in three attempts. Consider the variable x = amount of donation for a person selected at random from the population of last year's graduates of this university. (a) Write a few sentences describing what donation amounts you would expect to see if the value of x was observed for each of 1,000 graduates. to donate $25, and roughly $10 $25 $50 (c) What is P(x ≥ 25)? You would expect roughly of the graduates to donate nothing, roughly frequencies would be close to, but not exactly, these values. The four frequencies would add to (d) What is P(x > 0)? 0.05 (b) What is the most…

Use the following for the next 3 problems. Is there a difference in the amount of airborne bacteria between carpeted and uncarpeted rooms? In an experiment, 7 rooms were carpeted and 7 were left uncarpeted. The rooms are similar in size and function. After a suitable period of time, the concentration of bacteria in the air was measured (in units of bacteria per cubic foot) in all of these rooms. Assume the populations are normally distributed. The following is a summary of the data: Carpeted rooms: Uncarpeted rooms: X 184 175 S 22.0 16.9 19. A 95% confidence interval for the difference in mean bacterial concentration in the air of carpeted rooms versus uncarpeted rooms is (use 11 degrees of freedom). O -7.47 to 31.47. O -18.89 to 42.89. O 16.66 to 34.66. O 14.02 to 32.01.

he following table shows the returns of two types of investments, stocks (x) and bonds (y), under two different scenarios: boom and recession. The frequency f(∙) indicated the probability of boom and recession, and it is the same for any type of investment. Suppose you diversify your investments by splitting your funds half and half between stocks and bonds. That is, z = 1⁄2x + 1⁄2y. Find E(z) and the riskiness (standard deviation) of z.

I need the answer as soon as possible

4. In the study of human metabolism, it is known that daily calorie intake of a person age 25 above primarily affects the variability in weight gain. Scientists conducted an experiment to come up with a working formula of how much will be the average weight y (in kgs.) of a person age 25 if the person regularly has x calories of daily net calorie intake. It was shown that, on the average, y is related to x by the following relationship Y = In [x+ sin² (7)] + 50, x > 1. It was also observed that the each year the average weight of a person age 25 changes at a rate 1.5 kgs. per year. How fast is the average daily net calorie intake of a person changing when the person has 4 calories of daily net calorie intake?

At the bus station, there are six lines for arriving passengers, each staffed by a single worker. The arrival rate for passengers is 108 per hour and each passenger takes (on average) 3.1 minutes for a worker to process. The coefficient of variation for arrival time is 1.5 and the coefficient of varlation for service time is 1.1. (Round your answer to three decimal places.) On average, how many customers will be waiting in the queue? passengers

A light fixture contains five lightbulbs. The lifetime of each bulb is exponentially distributed with mean 199.0 hours. Whenever a bulb burns out, it is replaced. Let T be the time of the first bulb replacement. Let Xi, i = 1, . . . , 5, be the lifetimes of the five bulbs. Assume the lifetimes of the bulbs are independent.   1. Find P( X1 > 100). (Round the final answer to four decimal places.) 2. Find P( X1 > 100 and   X2 > 100 and • • • and   X5 > 100). (Round the final answer to four decimal places.) 3. Find P(T ≤ 100). (Round the final answer to four decimal places.) 4. Let t be any positive number. Find P(T ≤ t), which is the cumulative distribution function of T. 5. Find the mean of T. (Round the final answer to two decimal places.)

please solve a and b.