An oil company is considering introducing an additive into its gasoline, hoping to increase the average mileage per liter The engineers at the oil company's group are considering introducing an additive into their gasoline, hoping to increase the average mileage per liter. The research group's engineers tested engineers tested 32 cars with regular gasoline and another 39 cars with gasoline containing the additive. With the additive. From previous studies it is estimated that: Mileage per liter without additive: μ = 14.2 km, s = 3.24 km Mileage per liter with additive: Ju= 15.4 km, s = 5.56 km. a) What is the probability that the average kilometers traveled per liter in the sample of cars with additive is greater than 14.8 km? of cars with additive is greater than 14.8 km? b) If it is estimated that the variances of the kilometers traveled with and without additive are the same, what is the probability that in the samples, the average kilometers traveled per liter with the new additive will be greater than 14.8 km? per liter with the new additive is greater than the average kilometers traveled per liter without additive? liter without additive? c) If the variances of the kilometers traveled with and without additive are estimated to be the same, what is the probability that in the samples the standard deviation of the kilometers traveled per liter with the new additive is greater than the average kilometers traveled per liter without additive? kilometers traveled per liter with the new additive is 1.4 times smaller than the standard deviation of the kilometers traveled per liter without the new additive? kilometers traveled per liter without additive?
An oil company is considering introducing an additive into its gasoline, hoping to increase the average mileage per liter The engineers at the oil company's group are considering introducing an additive into their gasoline, hoping to increase the average mileage per liter. The research group's engineers tested engineers tested 32 cars with regular gasoline and another 39 cars with gasoline containing the additive. With the additive. From previous studies it is estimated that: Mileage per liter without additive: μ = 14.2 km, s = 3.24 km Mileage per liter with additive: Ju= 15.4 km, s = 5.56 km. a) What is the probability that the average kilometers traveled per liter in the sample of cars with additive is greater than 14.8 km? of cars with additive is greater than 14.8 km? b) If it is estimated that the variances of the kilometers traveled with and without additive are the same, what is the probability that in the samples, the average kilometers traveled per liter with the new additive will be greater than 14.8 km? per liter with the new additive is greater than the average kilometers traveled per liter without additive? liter without additive? c) If the variances of the kilometers traveled with and without additive are estimated to be the same, what is the probability that in the samples the standard deviation of the kilometers traveled per liter with the new additive is greater than the average kilometers traveled per liter without additive? kilometers traveled per liter with the new additive is 1.4 times smaller than the standard deviation of the kilometers traveled per liter without the new additive? kilometers traveled per liter without additive?
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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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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Transcribed Image Text:An oil company is considering introducing an additive into its gasoline, hoping to increase the
average mileage per liter.. The engineers at the oil company's group are considering
introducing an additive into their gasoline, hoping to increase the average mileage per liter. The
research group's engineers tested engineers tested 32 cars with regular gasoline and another
39 cars with gasoline containing the additive. With the additive. From previous studies it is
estimated that:
Mileage per liter without additive: μ = 14.2 km, s = 3.24 km
Mileage per liter with additive: u = 15.4 km, s = 5.56 km.
a) What is the probability that the average kilometers traveled per liter in the sample of cars
with additive is greater than 14.8 km? of cars with additive is greater than 14.8 km?
b) If it is estimated that the variances of the kilometers traveled with and without additive are
the same, what is the probability that in the samples, the average kilometers traveled per liter
with the new additive will be greater than 14.8 km? per liter with the new additive is greater
than the average kilometers traveled per liter without additive? liter without additive?
c) If the variances of the kilometers traveled with and without additive are estimated to be the
same, what is the probability that in the samples the standard deviation of the kilometers
traveled per liter with the new additive is greater than the average kilometers traveled per liter
without additive? kilometers traveled per liter with the new additive is 1.4 times smaller than
the standard deviation of the kilometers traveled per liter without the new additive?
kilometers traveled per liter without additive?
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VIEWStep 2: Determine the probability that sample of cars with additive travelled greater than 14.8 km.
VIEWStep 3: Perform the hypothesis test for two independent samples assuming equal variances.
VIEWStep 4: Determine the required probability using the F test for two variances.
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