Statistics II20805 marksNumerical: central limit theoremCentral Limit Theorem
Define Central limit theorem. The life of a certain brand of an electric bulb may be considered a random variable with mean 1350 hours and standard deviation 550 hours. Using central limit theorem, find the probability that the average life time of 100 bulbs exceeds 1440 hours.
Define Central limit theorem. The life of a certain brand of an electric bulb may be considered a random variable with mean 1350 hours and standard deviation 550 hours. Using central limit theorem, find the probability that the average life time of 100 bulbs exceeds 1440 hours. [5]
Given data: - Population mean: $\mu = 1350$ hours - Population standard deviation: $\sigma = 550$ hours - Sample size: $n = 100$ bulbs - Value tested: $\bar{X} = 1440$ hours - Required: $P(\bar{X} 1440)$ All data present. The Central Limit Theorem (CLT) states that if random samples of size $n$ a...