C Secure https//www-awh.aleks.com/alekscgi/x/lslexe/1o u slkasNW8 ydk Math 063-1
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Question
C Secure https//www-awh.aleks.com/alekscgi/x/lslexe/1o u slkasNW8 ydk Math 063-109 Statistics TTh 12 7(Sections 7:1-?-1130120 10 The Credit Risk Department of a major bank estimates the def $10,000 next month. ault rate on loans under $10,000 to be 5%. The bank will make 1900 loans that are under 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(p 004), which is the probability that 4% or fewer of next month's loans under Sla00 will be defaulted on. Round your answer to four decimal places. a. 0.05
Explanation / Answer
From the given problem, it seems that the data is from binomial distribution.
We have sample size = 1900, probability of defaulting loan is 5% = 0.05.
a.Mean(Proportion) = n*p = 1900*0.05 = 95
b.V(p) = n*p*(1-p)
=1900*0.05*0.95
=90.25
c.Here, we need to compute the cdf of x at m = 4 like p(X <= m)
=P(p< = 0.04) =P(X < = 76) where x number of defaulters and 76 is number of defaulters for proportion = 0,04.
= BINOMDIST(76, 1900, 0.05, TRUE) in excel
Where 400 is number of successes, 10000 is total number of trials, probability of success (here consider it as probability of defaulting loan), TRUE is for cumulative probability (i.e. cdf).
Thus, P(X < = 76) =P(p < = 0.04) = 0.0229
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