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Q4 i) To check the effectiveness of two brands of refrigerators, time taken for ice cubes to be formed from water in the freezer was compared. Two independent experiments based on 15 refrigerators of each brand were performed and time taken in formation of ice cubes was recorded. Suppose the population variance for both brands is 1.0 hour. Assuming normal distribution and mean time for both brands is equal to 20 hours, find the, a) Probability that the average time taken by brand A (XA) is higher than average time taken by B brand (XR) is at least 1.0 hour. Probability that X, will deviate from Xg by at least 45 minutes. How would your answer change if the underlying distribution was not b) c) normal?

Q4 i) To check the effectiveness of two brands of refrigerators, time taken for ice cubes to be formed from water in the freezer was compared. Two independent experiments based on 15 refrigerators of each brand were performed and time taken in formation of ice cubes was recorded. Suppose the population variance for both brands is 1.0 hour. Assuming normal distribution and mean time for both brands is equal to 20 hours, find the, a) Probability that the average time taken by brand A (XA) is higher than average time taken by B brand (XR) is at least 1.0 hour. Probability that X, will deviate from Xg by at least 45 minutes. How would your answer change if the underlying distribution was not b) c) normal?

A First Course in Probability (10th Edition)
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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Q4 i) To check the effectiveness of two brands of refrigerators, time taken for ice cubes to be formed from water in the freezer was compared. Two independent experiments based on 15 refrigerators of each brand were performed and time taken in formation of ice cubes was recorded. Suppose the population variance for both brands is 1.0 hour. Assuming normal distribution and mean time for both brands is equal to 20 hours, find the, a) Probability that the average time taken by brand A (XA) is higher than average time taken by B brand (XR) is at least 1.0 hour. Probability that XA will deviate from Xg by at least 45 minutes. How would your answer change if the underlying distribution was not b) c) normal? ii) Find a maximum likelihood estimator of u for a random sample of X1, X2, ..., Xn taken from a Poisson distribution. Clearly write all the steps. iii) a) If X is distributed as normal with u= 40 and o²=4, compute three values of the random variable X that divide the distribution in four equal parts. b) Find k such that P (k< T <-1.729) =0.049 for a random sample of size 20 taken from a normal distribution with T = s/Vn
Transcribed Image Text:Q4 i) To check the effectiveness of two brands of refrigerators, time taken for ice cubes to be formed from water in the freezer was compared. Two independent experiments based on 15 refrigerators of each brand were performed and time taken in formation of ice cubes was recorded. Suppose the population variance for both brands is 1.0 hour. Assuming normal distribution and mean time for both brands is equal to 20 hours, find the, a) Probability that the average time taken by brand A (XA) is higher than average time taken by B brand (XR) is at least 1.0 hour. Probability that XA will deviate from Xg by at least 45 minutes. How would your answer change if the underlying distribution was not b) c) normal? ii) Find a maximum likelihood estimator of u for a random sample of X1, X2, ..., Xn taken from a Poisson distribution. Clearly write all the steps. iii) a) If X is distributed as normal with u= 40 and o²=4, compute three values of the random variable X that divide the distribution in four equal parts. b) Find k such that P (k< T <-1.729) =0.049 for a random sample of size 20 taken from a normal distribution with T = s/Vn
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