Assume that in a certain company the average number of hours worked in a week by the workers is normally distributed (approximately), with a mean of (mu) = 56.4 and a standard deviation of (sigma) = 6.2. a,b) Find each of the following probabilities for a randomly selected worker a) Probability of working more than an average of 62 hours per week b) Probability of working less than an average of 45 hours per week c) We want to make the statement that 98% of the workers work between 40 hours per week and N hours per week. What value for N will make this an accurate statement?
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!
normal distribution, word problem
Assume that in a certain company the average number of hours worked in a week by the workers is
a mean of (mu) = 56.4 and a standard deviation of (sigma) = 6.2.
a,b) Find each of the following probabilities for a randomly selected worker
a)
b) Probability of working less than an average of 45 hours per week
c) We want to make the statement that 98% of the workers work between 40 hours per week and N hours per week.
What value for N will make this an accurate statement?
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