Using the normal distribution to approximate binomial probabilities Corporate bo

Question

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 69% of Caa-C-rated corporate bonds defaulted, whereas only 17% of Caa-C-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 Caa-C-rated corporate 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. Use the normal distribution to approximate the probability of obtaining exactly 140 defaults in the sample. The probability is ___. What is the probability that the sample contains 130 or fewer defaults? 0.1251 0.8749 0.1093 0.8907

Explanation / Answer

p = .69 for Caa Crated corp. bonds default.

1st part

n = 200

Expected value = np = .69*200 = 138

Stdev = sqrt(npq) = sqrt(.69*200*.31) = 6.54

2nd part:

P(X=140) = P(Z = 140-125 / 7.5) = P(Z=2) = .025

P(X<=130) = P(Z<= 130-125 / 7.5) = P(Z<= .667) = .7486.

I dont see a value matching this, but I know for sure with the params givin this answer is right

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