Without doing any computation, decide which has a higher probability, assuming each sample is from a population that is normally distributed with u= 100 and o = 15. Explain your reasoning. (a) P(90 sxs 110) for a random sample of size n= 10 (b) P(90 sxs110) for a random sample of size n= 20 Choose the correct answer below. O A. P(90 s xS 110) for a random sample of size n= 10 has a higher probability. As n increases, the standard deviation increases. O B. P(90 s xS110) for a random sample of size n= 20 has a higher probability. As n increases, the standard deviation decreases. OC. P(90 sxs 110) for a random sample of sizen=20 has a higher probability. As n increases, the standard deviation increases. O D. P(90 sxs 110) for a random sample of size n=10 has a higher probability. As n increases, the standard deviation decreases.
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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