You may need to use the appropriate appendix table or technology to answer this question. The life expectancy of a certain country is 79 with a standard deviation of 6 years. A random sample of 64 individuals is selected. (Round your answers to four decimal places.) (a) What is the probability that the sample mean will be larger than 81 years? (b) What is the probability that the sample mean will be less than 77.5 years? (c) What is the probability that the sample mean will be between 77 and 82 years? (d) What is the probability that the sample mean will be between 76 and 78 years? (e) What is the probability that the sample mean will be larger than 77 years?
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
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