ndent 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 me
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)
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