For all of the California Community Colleges, the population of full-time faculty members have a mean age of 46.2 years with a standard deviation of 7.4 years. Assume that the ages of full-time faculty members is normally distributed. If a sample of 10 full-time faculty members are selected from a California Community College, what is the probability that the sample full-time faculty member will have a sample mean age younger than 40 years old (have a sample mean age less than 40 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!
For all of the California Community Colleges, the population of full-time faculty members have a mean age of 46.2 years with a standard deviation of 7.4 years. Assume that the ages of full-time faculty members is
If a sample of 10 full-time faculty members are selected from a California Community College, what is the
Type in your final decimal solution for the probability rounded to four decimal places.
P(x¯<40)= ____________
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