Math CentralQuandaries & Queries


Question de m.j., student :

Car Loan Rates The national average for a new car loan was 8.28%. If the rate is normally distributed with a standard deviation of 3.5%, find these probabilities.
a. One can receive a rate less than 9%.
b. One can receive a rate less than 8%.

Hi MJ,

My bank says that their rates are normally distributed with a mean of 7.5% and a standard deviation of 2.0%. What is the probability that I will receive a rate of less than 7%?

Let X be the random variable that is the rate I receive. I want Pr[X < 0.07]. To use the standard normal tables I need to convert X to the standard normal variable using

Z = (X - μ)/σ

Thus in my case

Pr[X < 0.07] = Pr[Z < (0.07 - 0.075)/0.02] = Pr[Z < - 0.25]

Since the standard normal distribution is symmetric around zero

Pr[Z < - 0.25] = Pr[Z > 0.25]

My standard normal table gives me

Pr[0 < Z < 0.25] = 0.0987

and hence

Pr[Z > 0.25] = 0.5 - 0.0987 = 0.4013

Now try your problem,

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