A new muscle relaxant is available. Researchers from the firm developing the relaxant have done studies that indicate that the time lapse between administration of the drug and beginning effects of the drug is normally distributed, with mean ? = 38 minutes and standard deviation ? = 5 minutes. (a) The drug is administered to one patient selected at random. What is the probability that the time it takes to go into effect is 35 minutes or less? (Use 3 decimal places.) (b) The drug is administered to a random sample of 10 patients. What is the probability that the average time before it is effective for all 10 patients is 35 minutes or less? (c) Comment on the differences of the results in parts (a) and (b). The probability in part (b) is ---Select--- smaller than larger than the same as part (a) because the ---Select--- mean standard deviation is ---Select--- smaller larger for the x distribution.
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!
A new muscle relaxant is available. Researchers from the firm developing the relaxant have done studies that indicate that the time lapse between administration of the drug and beginning effects of the drug is
(b) The drug is administered to a random sample of 10 patients. What is the probability that the average time before it is effective for all 10 patients is 35 minutes or less?
(c) Comment on the differences of the results in parts (a) and (b).
The probability in part (b) is ---Select--- smaller than larger than the same as part (a) because the ---Select--- mean standard deviation is ---Select--- smaller larger for the x distribution.
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