The Credit Risk Department of a major bank estimates the default rate on loans under $10,000 to be 5%. The bank will make 1900 loans that are under $10,000 next month. Answer the following. (If necessary, consult a list of formulas.) (a)Find the mean of p , where p is the proportion of defaults on the 1900 loans under $10,000 to be made next month. (b)Find the standard deviation of p . (c)Compute an approximation for P≤p0.04 , which is the probability that 4% or fewer of next month's loans under $10,000 will be defaulted on. Round your answer to four decimal places
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!
Answer the following. (If necessary, consult a list of formulas.)
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(a)Find the mean of
p
p
1900
$10,000
(b)Find the standard deviation of
p
(c)Compute an approximation for
P≤p0.04
4%
$10,000
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