Aa Aa E 9. Using the normal distribution to approximate binomial probabilities C

Question

Aa Aa E 9. Using the normal distribution to approximate binomial probabilities Corporate bonds have higher default rates than municipal bonds with the same rating. Moody's Investors Service measured 10-year default rates for bonds between 1970 and 2006. They found that 43% of B-rated corporate bonds defaulted, whereas only 12% of B-rated municipal bonds defaulted. [Source: Moody's Investors Service, The U.S. municipal bond rating scale: Mapping to the global rating scale and assigning global ratings to municipal obligations (Moody's Investors Service, 2007). A random sample of 200 B-rated municipal bonds is selected. Of the 200 bonds in the sample, the expected number of defaults (during the next 10 years) is and the standard deviation of the number of defaults is Use the Distributions tool to help you answer the questions that follow. Normal Distribution Mean 35 Standard Deviation 5.5 10 20 40 50 60 70 80 90 100 30 Use the normal distribution to approximate the probability of obtaining exactly 28 defaults in the sample. The probability is

Explanation / Answer

expected number of defaults =np=200*0.12=24

std deviation=(np(1-p))1/2 =4.5957

P(X=28)= P(27.5<X<28.5)=P((27.5-24)/4.5957<Z<(28.5-24)/4.5957)=0.8363-0.7768=0.0594

P(X<=17)=P(Z<-1.4144)=0.0793

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