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 (x̄A) is higher than average time taken by B brand (x̄B) is at least 1.0b) Probability that x̄a will deviate from x̄b 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 σ²=4, compute three values of the random variable X that divide the distribution in four equal pb)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= = (x̄-μ) /(s/√n) i) To check the effectiveness of two brands of refrigerators, time taken for ice cubes tobe formed from water in the freezer was compared. Two independent experimentsbased on 15 refrigerators of each brand were performed and time taken in formation ofice 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, findthe,а)Probability that the average time taken by brand A (XA) is higher than averagetime taken by B brand (Xg) is at least 1.0 hour.b)Probability that X will deviate from X, by at least 45 minutes.c)How would your answer change if the underlying distribution was notnormal?ii) Find a maximum likelihood estimator of u for a random sample of X1, X2, ..., Xntaken 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 therandom 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 takenfrom a normal distribution with T =s/Vn

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Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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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 (x̄A) is higher than average time taken by B brand (x̄B) is at least 1.0

b) Probability that x̄a will deviate from x̄b 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 σ²=4, compute three values of the random variable X that divide the distribution in four equal p

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= = (x̄-μ) /(s/√n)

Transcribed Image Text: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) Probability that the average time taken by brand A (XA) is higher than average time taken by B brand (Xg) is at least 1.0 hour. b) Probability that X will deviate from X, 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. 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

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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