Over the year, projected due dates for expectant mothers have been notoriously bad at a large metropolitan hospital. The numbers of days to birth beyond the projected due date are known to be equally likely between 0 days and 40 days. a. Find the expected value and variance of the number of days to birth beyond the projected due date. b. If a random sample of 50 expectant mothers is taken, what is the probability that, on average, the births occur more than 2 weeks after the projected due dates? c. Hospital management has decided that, if the average number of days to birth beyond the projected due date for the sample taken is in the top 10%, a new forecasting technique will be developed in order to predict the expectant mothers’ due dates. What is the minimum average number of days to birth beyond the projected due date allowed that will prompt management to develop a new due date projection technique?
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!
Over the year, projected due dates for expectant mothers have been notoriously bad at a large metropolitan hospital. The numbers of days to birth beyond the projected due date are known to be equally likely between 0 days and 40 days.
a. Find the expected value and variance of the number of days to birth beyond the projected due date.
b. If a random sample of 50 expectant mothers is taken, what is the probability that, on average, the births occur more than 2 weeks after the projected due dates?
c. Hospital management has decided that, if the average number of days to birth beyond the projected due date for the sample taken is in the top 10%, a new forecasting technique will be developed in order to predict the expectant mothers’ due dates. What is the minimum average number of days to birth beyond the projected due date allowed that will prompt management to develop a new due date projection technique?
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