Compute P(X) using the binomial probability formula. Then determine whether the normal distribution can be used to estimate this probability. If so, approximate P(X) using the normal distribution and compare the result with the exact probability. n= 48, p=0.3, and X=6 For n= 48, p=0.3, and X=6, find P(X). P(X) = (Round to four decimal places as needed.) Can the normal distribution be used to approximate this probability? O A. Yes, the normal distribution can be used because np(1 -p) 2 10. O B. Yes, the normal distribution can be used because np(1-p)s 10. OC. No, the normal distribution cannot be used because np(1-p)< 10. O D. No, the normal distribution cannot be used because np(1-p)2 10. Approximate P(X) using the normal distribution. Select the correct choice below and fill in any answer boxes in your choice. O A. P(X) = (Round to four decimal places as needed.) O B. The normal distribution cannot be used. By how much do the exact and approximated probabilities differ? Select the correct choice below and fill in any answer boxes in your choice. O A. (Round to four decimal places as needed.) The normal distribution cannot be used.
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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