25 38 26 31 21 46 29 19 35 39 24 21 17 42 46 19 50 40 43 34 31 51 36 32 18 29 22 21 24 39 46 31 33 34 30 30
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!
Oakdale Furniture Company uses a special type of woodworking glue in the assembly of its furniture. During the past 36 weeks, the following amounts of glue (in gallons) were used by the company: (given)
a. Compute the mean and the standard deviation of this sample.
b. Consider the following class intervals for the number of gallons used each week:
Less than 20.
20–27.
28–33.
34–37.
38–43.
More than 43.
Determine the proportion of data points that fall into each of these intervals. Compare these proportions to the probabilities that a normal variate with the mean and the standard deviation you computed in part (a) falls into each of these intervals. Based on the comparison of the observed proportions and those obtained from assuming a
c. Assume that the numbers of gallons of glue used each week are independent random variables, having the normal distribution with mean and standard deviation computed in part (a). What is the probability that the total number of gallons used in six weeks does not exceed 200 gallons? (Hint: The mean of a sum of random variables is the sum of the means and the variance of a sum of independent random variables is the sum of the variances.)
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