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Normal Probability

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The credit score of a 35 applying for a mortgage is normally distributed with a mean score of 600 and a standard deviation of 100.
What credit score defines the top five percent of scores.
Within what range would 85% of credit score fall.

One hundred car tires are tested and the mean useful life comes out to 50,000 and the sample standard deviation is 5,000 miles.
Develop a 95% confidence interval for the mean useful life of all car tires.
Develop a 90% confidence interval?

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Solution Summary

Normal probability within what range would credit scores fall are determined.

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Standard deviation
The credit score of a 35 applying for a mortgage is normally distributed with a mean score of 600 and a standard deviation of 100.
Answers
Let X be the credit score of those applying for a mortgage. Given that X is normal with mean µ = 600 and standard deviation  = 100.
Standardizing the variable X using and from standard normal tables, we have,
What credit score defines the top five percent of scores?
Here we need a value of X say K such that P (X > K) = 0.05
We know P (Z > 1.645) = 0.05
Thus from Z score of K we have,
Solving for K we have K = 764.5
Hence the credit score defines the top five percent of scores = 764.5

Within what ...

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