1 Which distribution?Each of the following random variables has a named distribution we studied in class. Give the namof the distribution, and the values of its parameters.A standard economic model of consumption of household goods assumes that productsare consumed at a constant average rate, but with random and independent times between usage.To model inter-purchase times, we also take into account the amount purchased at once.For concreteness, suppose that a customer with a cold purchases a box of 120 tissues, and uses anaverage of 2 tissues every hour. T is the time (in minutes) until the entire box of tissues is usedup, and another box must be purchased.A busy office receives an average of 100 calls per hour. C is the number of calls receivedover a particular 5-minute interval.One possible betting strategy in roulette is to take all your money and bet it on red;you have a chance of winning such a bet. If you win, then you bet all the money you have again,and so on, until you lose. This is not a very good strategy.B is the number of bets you make before you lose all your money.

Given 3 examples of random variables, those have a named distribution.

Answered: 1 Which distribution? Each of the…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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The price to earnings ratio (P/E) Is an Important tool in financial work. A random sample of 14 large U.S. banks (JP Morgan Chase, Bank of America, and others) gave the following P/E ratios.t 24 16 22 14 12 13 17 22 15 19 23 13 11 18 The sample mean is x = 17.1. Generally speaking, a low P/E ratio indicates a "value" or bargain stock. Suppose a recent copy of a magazine indicated that the P/E ratio of a certain stock index is H = 18. Let x be a random variable representing the P/E ratio of all large U.S. bank stocks. We assume that x has a normal distribution and o = 4.7. Do these data indicate that the P/E ratio of all U.S. bank stocks is less than 18? Use a = 0.01. (a) What is the level of significance? State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? O Ho: H = 18; H1: H # 18; two-tailed O Ho: H = 18; H1: H 18; right-tailed %3D O Ho: H # 18; H1: H = 18; two-tailed (b) What sampling distribution will you use? Explain the rationale…
A random sample of 15 families representing three social classes has been observed for the frequency with which the parents administer physical punishment to the children over a period of a week. Are the differences significant? Use the five-step model as a guide and write a sentence or two of interpretation for your results. Working Class Middle Class Upper Class 10 11 7 9 10 5 4 5 2 2 2 0 1 0 0
Reaction time (in milliseconds) with and without TMS ID # TMS No TMS 1 490 520 580 550 3 460 540 4 520 500 5 490 520 490 520 7 520 480 8 500 530 490 500 10 460 500 11 500 520 0. Table 4.10 shows the weights of 20 mice. Find the mean, median, and mode. Is the distribution of weights normal in shape or skewed? Table 4.12 Salary at "Chocolate Daydreams" Bakery for all 10 employees Staff ID 1 2 3 4 5 6. 7 8 9. 10 Salary 15k 18k 16k 14k 15k 15k 12k 17k 90k 95k a. What is the mean salary at the bake b. Is the mean the best measure of central tendency for this data set? Why or why not? c. What measure of center might provide a better representation of the center of this data set? d. Calculate the other measure of center. e. How much does this other measure of center differ from the mean?
Matthew the Barber owns a one-chair shop. At barber college, they told Matthew that his customers would exhibit a Poisson arrival distribution and that he would provide an exponential service distribution. His market survey data indicate that customers arrive at a rate of two per hour. It will take Matthew an average of 20 minutes to give a haircut. Based on these figures, find the following: Part (a): The average number of customers waiting. Part (b): The average time a customer waits. Part (c): The average time a customer is in the shop. Part (d): The average utilization of Matthew's time.
In the US, 46.2% of all people have type O blood, 39.1% have type A blood, 10.4% have type B blood and 4.3% have type AB blood. A researcher wants to see if the distribution of blood type is different for millionaires. The table below shows the results of a random sample of 3116 millionaires. What can be concluded at the a = 0.01 significance level? a. Complete the table by filling in the expected frequencies. Round to the nearest whole number: Frequencies of Blood Type Outcome Frequency Expected Frequency 1434 A 1224 В 310 AB 148 b. What is the correct statistical test to use? Select an answer V c. What are the null and alternative hypotheses? Но: O Blood type and income are independent. O The distribution of blood type for millionaires is not the same as it is for Americans in general. O The distribution of blood type for millionaires is the same as it is for Americans in general. O Blood type and income are dependent.
The price of a share of stock divided by the company's estimated future earnings per share is called the P/E ratio. High P/E ratios usually indicate "growth" stocks, or maybe stocks that are simply overpriced. Low P/E ratios indicate "value" stocks or bargain stocks. A random sample of 51 of the largest companies in the United States gave the following P/E ratiost. 9 20 11 35 19 13 15 21 29 53 16 26 21 14 21 27 10 12 47 14 40 18 60 72 33 14 8 49 5 16 8 19 12 31 67 51 26 18 17 20 19 13 25 23 27 44 20 27 19 18 32 (a) Use a calculator with mean and sample standard deviation keys to find the sample mean x and sample standard deviation s. (Round your answers to one decimal place.) (b) Find a 90% confidence interval for the P/E population mean u of all large U.S. companies. (Round your answers to one decimal place.) lower limit upper limit (c) Find a 99% confidence interval for the P/E population mean u of all large U.S. companies. (Round your answers to one decimal place.) lower limit upper…
The table shows population statistics for the ages of Best Actor and Best Supporting Actor winners at an awards ceremony. The distributions of the ages are approximately bell-shaped. Compare the z-scores for the actors in the following situation. Best actor Best supporting actor u= 41.0 u=55.0 Q= 7.7 Q= 12 In a particular year, the Best Actor was 44 years old and the best supporting actor was 42 years old. Determine the z-scores for each. best actor z=____________ best supporting actor z=___________ Round to two decimal places as needed.
Students arrive one at a time, completely at random, to an advice clinic at a rate of10 per hour. Students take on average 5 minutes of advice but there is wide variation inthe time they need; this variation may be well modeled by the exponential distribution.a. Assume there is only one advisor serving in the clinic. Find the followingexpected measures of performance for this system: the expected time in the clinic, theexpected time in the queue for advice, the expected number of students in the clinic,and the expected number of students waiting for advice.
Consider a 100-point college exam for which there is a large number of students that perform extremely well, as well as a large number of students that perform extremely poorly. Which statement below is true? O The distribution of scores is probably symmetrical. O The distribution of scores probably has a mean close to 75. O The distribution of scores is probably bimodal. O The distribution of scores probably has a median close to 75,
The city of Oakville has 60000 households. A social researcher from the University of Toronto collected a simple random sample of 100 households. Let the auxiliary variable x be the number of persons living in the household and y be the weekly spending for food. The researcher obtained the following sample statistics: 100 100 2 X; = 320 yi = 10000 E09 x? = 1250 100 E09 y? = 1100000 E00 x;y; = 36000 Ty = 150000 Sx = 1.5 Sy = 31.8 (a) Using the ratio estimation, estimate the mean weekly spending for food and place a bound on the error of estimation. You need to report the numerical values. Show all the steps. Circle the final answer. (b) Using the regression estimation, estimate the total weekly spending for food and place a bound on the error of estimation. You need to report the numerical values. USE MSE = 5200. Show all the steps. Circle the final answer.
A dietician wishes to see if a person’s cholesterol level will decrease if the diet is supplemented by a certain mineral. Six randomly selected subjects were pretested, and then they took the mineral in supplement for a 6-week period. The results are shown in the table (cholesterol is measured in milligrams per deciliter). Assume preliminary analysis indicate the differences come from a normally distributed population. Subject Before After Difference 1 210 190 20 2 235 170 65 3 208 210 -2 4 190 188 2 5 172 173 -1 6 244 228 16 Use the paired t-test to answer the following: at the 10% significance level, do the data provide sufficient evidence to conclude that the mean cholesterol level was greater before the mineral was supplemented than after? Write the hypotheses for the paired t-test. H0:___________________________ Ha:__________________________________ compute the test statistic. Round to one decimal place determine the p-value.
To determine whether caffeine consumption affects the ability to solve math problems, a researcher had one group solve math problems after taking a cup of caffeinated drink and another group solves math problems after taking a cup of water. The group who took the caffeinated drink completed 35 problems in one hour and the group that had water completed 20 problems in one hour. Assuming the number of problems solved is normally distributed in each group, what statistical test would be used to test the research hypothesis? Explain your answer.

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