Chapters: Normal and Exponential random variables. Q: Econo-Tire is planning on advertising campaign for its newest product, an inexpensive radial. Preliminary road tests conducted by the firm’s quality-control department have suggested that the lifetimes of a set of these tires will be normally distributed with an average of 30,000 miles and a standard deviation of 5000 miles. a. The marketing division would like to run a commercial that makes the claim that at least nine out of ten drivers will get at least 25,000 miles for a set of Econo Tires. Based on the road test data, is the company justified in making that assertion? b. What mileage corresponds to the 25th percentile for tire lifetime

Chapters: Normal and Exponential random variables. Q: Econo-Tire is planning on advertising campaign for its newest product, an inexpensive radial. Preliminary road tests conducted by the firm’s quality-control department have suggested that the lifetimes of a set of these tires will be normally distributed with an average of 30,000 miles and a standard deviation of 5000 miles. a. The marketing division would like to run a commercial that makes the claim that at least nine out of ten drivers will get at least 25,000 miles for a set of Econo Tires. Based on the road test data, is the company justified in making that assertion? b. What mileage corresponds to the 25th percentile for tire lifetime

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 ideal serving temperature of a particular type of red wine in 13 °C. A food critic is worried that even high-profile restaurants are unaware of this important fact and tend to serve this type of wine at a temperature that is too warm. He randomly selects 6 of the best restaurants, orders a bottle of this wine at each place, and measures the serving temperature with a precision thermometer. The mean temperate in his sample is 17.17 °C and the standard deviation is 3.69 °C. The food critic wishes to conduct a test at the .05 level of significance to see if these results provide evidence that the true mean serving temperature is indeed above 13 °C. Calculate the value of the test statistic. (Provide your answer as a number rounded to 3 decimals.)
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Jessica Salas, President of Salas Products, is reviewing the warranty policy for her company's new model of automobile batteries. Life tests performed on a sample of 100 batteries indicated: (1) an average life of 75 months, (2) a standard deviation of 5 months, and (3) a bell-shaped battery life distribution. What percentage of the batteries will fail within the first 65 months of use? 5% 1% 0.5% 7.5% 2.5%
1. The fuel efficiency of a new model pick-up truck (truck) is measured in miles per gallon (mpg). A company claims that their new truck gets 25 mpg on average. A consumer group thinks the company is lying and claims that the mean mileage for all the trucks is less than 25 mpg. In a random sample, of forty-five of these trucks the mean mpg was 23.3 mpg with a standard deviation of 5.1 mpg. a. Conduct a hypothesis test to test the consumer group's claim at the 5% significance level. Be sure to state you Ho and Ha, your test statistic and p- value, whether or not you reject Ho and whether you support the claim. b. Write a complete sentence describing what a Type I error is in context. c. Write a complete sentence describing what a Type II error is in context.
Managers of an industrial plant want to determine which of two types of fuel, gas or electric, is more cost efficient (measured in cost per unit of energy). Independent random samples were taken of plants using electricity and plants using gas. These samples consisted of 10 plants using electricity, which had a mean cost per unit of $53.50 and standard deviation of $8.19 , and 11 plants using gas, which had a mean of $55.40 and standard deviation of $8.23 . Assume that the populations of costs per unit are normally distributed for each type of fuel, and assume that the variances of these populations are equal. Construct a 95% confidence interval for the difference −μ1μ2 between the mean cost per unit for plants using electricity, μ1 , and the mean cost per unit for plants using gas, μ2 . Then find the lower limit and upper limit of the 95% confidence interval. Carry your intermediate computations to at least three decimal places. Round your responses to at least…
2. "According to Dietary Goals for the US (1977), high sodium intake may be related to ulcers, stomach cancer, and migrane headaches. The human requirement for salt is less than 220 milligrams per day, which is surpassed in most single servings of ready-to-eat noodles. If a random sample of 21 similar servings of noodles has a mean sodium content of 200 milligrams and a standard deviation of 11.71 will you eat this noodles? Use 0.05 level of significance "a. "Based on empirical evidence, the sodium content of the noodles is within the acceptable range. Hence, I will eat the noodles."b. No sufficient data to prove the case.c. "I am 100% sure that the noodles? Useis not safe based on the statistical result. Hence, I will not eat the noodles."d. "It is safe to assume that the sodium content of the noodles is not less than the stated value. Hence, I won't eat it unless evidence suggest otherwise."
2. A travel agent claims that the mean price of a round trip flight from San Francisco to Hawaii is less than $510. A simple random sample of 60 round trip flights from San Francisco to Hawaii has a mean price of $502. Assume the population standard deviation is $110. At a significance level of 5%, is there enough statistical evidence to support the travel agent's claim? Requirements: 1. 2. 3. Step 1: State the hypothesis: Họ: Ha: Tail Step 2: Draw your distribution and find critical number(s) Step 3: Compute the test statistics Step 4: Make a Decision: Step 5: Summarize the result: (Restate the level of significance and discuss the claim)
A food distribution company claims that a restaurant chain receives, on average, 26 pounds of fresh vegetables on a daily basis. The standard deviation of these shipments is known to be 4.4 pounds. The district manager of the restaurant chain decides to randomly sample 35 shipments from the company and finds a mean weight of 24.7 pounds. Test at a 3% level of significance to determine whether or not the food distribution company sends less than 26 pounds of fresh vegetables. a. Check the TWO requirements that are satisfied. The Central Limit Theorem applies. The a distribution is normal since n > 30. The a distribution is normal since the x distribution is normal. The p distribution is normal since np > 5 and nq > 5.