The number N of devices that a technician must try to repair during the course of an arbitrary workday is a random variable having a geometric distribution with parameter p = 1/8. We estimate the probability that he manages to repair a given device to be equal to 0.95, independently from one device to another

a) What is the probability that the technician manages to repair exactly five devices, before his second failure, during a given workday, if we assume that he will receive at least seven out-of-order devices in the course of this particular workday?

b) If, in the course of a given workday, the technician received exactly ten devices for repair, what is the probability that he managed to repair exactly eight of those?

c) Use a Poisson distribution to calculate approximately the probability in part (b).

d) Suppose that exactly eight of the ten devices in part (b) have indeed been repaired. If we take three devices at random and without replacement among the ten that the technician had to repair, what is the probability that the two devices he could not repair are among those?

Answer each sub-question by stating whether the term indicated would increase, decrease, stay the same, or not enough info to say. (Note: “increase” and “decrease” refer to the absolute value.)

a) In the binomial distribution, as N decreases, what happens to the value of the most likely outcome when P = .50?

B. For any N, as P increases from .10 to .50, what happens to the value of the most likely outcome?

C. For any N, as P increases from .50 to .90, what happens to the value of the most likely outcome?

D. When P = .5, what happens to the probability of the most likely individual outcome, as N increases?

E. When P = .8, what happens to the probability of the most likely individual outcome, as N increases?

F. In the binomial distribution, what happens to the value of the most likely individual outcome as N increases and, at the same time, P increases?

G) When P = .5, what happens to the individual probabilities of the very most extreme outcomes (that is, the very highest and lowest possible outcomes) as N increases?

Please show work. Thank You.

A machine that fills beverage cans is supposed to put 12 ounces of beverage in each can. Following are the amounts measured in a simple random sample of eight cans: 12.15 12.17 12.20 11.88 12.16 12.04 12.05 12.11 Perform a hypothesis test to determine whether the mean volume is greater than 12 ounces. Use the α=0.05 level of significance and the critical value method. Compute the value of the test statistic. Round the answer to three decimal places. t=?

The World Bank collected data on the percentage of GDP that a country spends on health expenditures ("Health expenditure," 2013) and also the percentage of woman receiving prenatal care ("Pregnant woman receiving," 2013). The data for the countries where this information is available for the year 2011 are in table #10.1.8. Find the correlation coefficient and coefficient of determination and then interpret both.

The probability that a certain kind of flower seed will germinate is .80.

(a) If 194 seeds are planted, what is the probability that fewer than 141 will germinate? (Round standard deviation and your final answer to 4 decimal places.)

Probability()

(b) What is the probability that at least 141 will germinate? (Round standard deviation and your final answer to 4 decimal places.)

Probability ()

For the past 104 ​years, a certain state suffered 27 direct hits from major​ (category 3 to​ 5) hurricanes. Assume that this was typical and the number of hits per year follows a Poisson distribution. Complete parts​ (a) through​ (d). a) What is the probability that the state will not be hit by any major hurricanes in a single​ year? The probability is nothing.​ (Round to four decimal places as​ needed.) ​(b) What is the probability that the state will be hit by at least one major hurricane in a single​ year? The probability is nothing. ​(Round to four decimal places as​ needed.) Is this​ unusual? Yes No ​(c) What is the probability that the state will be hit by at least three major hurricanes in a single​ year, as happened last​ year? The probability is nothing. ​(Round to four decimal places as​ needed.) Does this indicate that the 2004 hurricane season in this state was​ unusual?

Phone calls arrive at the rate of 48 per hour at the reservation desk for Regional Airways.

a. Compute the probability of receiving four calls in a 5-minute interval of time.

b. Compute the probability of receiving exactly 9 calls in 15 minutes.

c. Suppose, no calls are currently on hold. If the agent takes 5 minutes to complete the current call, how many callers do you expect to be waiting by that time?

d. Suppose, no calls are currently on hold, If the agent takes 5 minutes to complete the current call, what is the probability that no callers will be waiting?

e. If no calls are currently being processed, what is the probability that the agent can take 3 minutes for personal time without being interrupted by a call?

A ski gondola carries passengers to the top of a mountain. A plaque states that its maximum capacity is 12 people or 2019 lbs. Men’s weights are normally distributed with a mean of 179 lbs and a standard deviation of 30 lbs.

a)

What is the probability that 12 randomly-selected men will exceed the weight limit of the gondola?

b)

Suppose you are the engineer in charge of safety at the mountain. What is the maximum number of men you would allow to ride the gondola at a time in order to be confident they would not exceed the weight limit? Explain.

c)

Suppose the gondola carries the maximum number of men (as given in part b) on every trip. The gondola operates for eight hours a day, and each trip takes 15 minutes to complete. What is the expected amount of time before you lose your licence? Does this answer lead you to rethink your answer to part b)? If so, what would you do differently in part b) (you don’t have to redo part b)?

Indicate using either a “B” (binomial) or a “P” (Poisson) which distribution you would use to predict random frequencies in the following data:

Number of teeth per person with cavities in the population
Number of times a fish inhales within a given time period
Number of Girl Scout cookie boxes sold in front of Walmart each day
Number of Drosophila legs with fewer than 5 bristles
Number of mitochondria in a cell

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 42% 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 128 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

3.27. Problem. (Section 11.5) The following are applications of Theorem 11.6 or the Central Limit Theorem.

(a) Determine the distribution of (1/5)X₁ + (2 /5)X₂ + (2/5)X₃ if X₁, X₂ and X₃ are independent normal distributions with µ = 2 and

σ = 3.

(b) The weight (kg) of a StarBrite watermelon harvested under certain environmental conditions is normally distributed with a mean of 8.0 with standard deviation of 1.9. Suppose 24 StarBrite watermelons grown in these conditions are harvested; compute the probability that the average weight of all 24 watermelons is less than 7.8 kg/fruit

(c) A study of elementary school students reports that the mean age at which children begin reading is 5.7 years with a standard deviation of 1.1 years. If 55 elementary school students are selected at random, approximate the probability that the average age at which these 55 children begin reading is at least 6.

(d) Let the random variable X be defined as the number of pips that show up when a fair, six-sided die is rolled. The mean and standard deviation of X can be shown to be µX = 3.5 and σX = 1.71, respectively. If 100 fair, six-sided dice are rolled, aproximate the probability that the mean of number of pips on the 100 dice is less than 3.25

What is the best statistical analysis to use when determining if verbal reinforcement affects response rates?

Come up with a research example (not in the text) of when it would be appropriate to use a repeated-measures design. Describe the study. Come up with a research example (not in the text) of when it would be appropriate to use a matched-pairs design. Describe the study. Come up with a research example (not in the text) of when it would be appropriate to use a pretest/posttest design. Describe the study. Imagine that you needed 10 pairs of scores in your matched-pairs study. How many different individuals would you need? Imagine that you needed 10 pairs of scores in your repeated-measures study. How many different individuals would you need? What is one of the benefits of choosing a related-samples design?

(2) Suppose the original regression is given by y = β0 + β1x1 + β2x2 + β3x3 + u. You want to test for heteroscedasticity using F test. What auxiliary regression should you run? What is the

null hypothesis you need to test?