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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 (XB) is at least 1.0 hour. b) Probability that X, will deviate from Xg by at least 45 minutes. c) How would your answer change if the underlying distribution was not 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 o?=4, compute three values of the random variable X that divide the distribution in four equal parts.

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 (XB) is at least 1.0 hour. b) Probability that X, will deviate from Xg by at least 45 minutes. c) How would your answer change if the underlying distribution was not 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 o?=4, compute three values of the random variable X that divide the distribution in four equal parts.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.3: Measures Of Spread
Problem 1GP
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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, а) time taken by B brand (XR) is at least 1.0 hour. Probability that the average time taken by brand A (XA) is higher than average Probability that X, will deviate from X, 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 µ 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 µ= 40 and o²=4, compute three values of the random variable X that divide the distribution in four equal parts.
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, а) time taken by B brand (XR) is at least 1.0 hour. Probability that the average time taken by brand A (XA) is higher than average Probability that X, will deviate from X, 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 µ 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 µ= 40 and o²=4, compute three values of the random variable X that divide the distribution in four equal parts.
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