Questions: Monthly Mortgage Payments The average monthly mortgage payment including principal and interest is 982 in the United States. If the standard deviation is approximately 180 and the mortgage payments are approximately normally distributed, find the probabilities. Use a TI-83 Plus/TI-84 Plus calculator and round the answers to at least four decimal places. Part 1 of 2 (a) The selected monthly payment is more than 1400. P(X>1400)=.0101 Alternate Answer: P(X>1400)=0.0101 Part 2 of 2 (b) The selected monthly payment is between 650 and 975. P(650<X<975)=

Solution Steps

To find the probability that the selected monthly payment is greater than \$1400, we first calculate the Z-score for \( X = 1400 \):

$$Z = \frac{X - \mu}{\sigma} = \frac{1400 - 982}{180} \approx 2.3222$$

Using the standard normal distribution, we find:

$$P(X > 1400) = 1 - P(Z < 2.3222) \approx 1 - 0.9899 = 0.0101$$

Next, we calculate the probability that the selected monthly payment is between \$650 and \$975. We find the Z-scores for both values:

For $X = 650$:

$$Z_{650} = \frac{650 - 982}{180} \approx -1.8444$$

For $X = 975$:

$$Z_{975} = \frac{975 - 982}{180} \approx -0.0389$$

Now, we can find the probability:

$$P(650 < X < 975) = P(Z < -0.0389) - P(Z < -1.8444) \approx 0.4841 - 0.0322 = 0.4519$$

Final Answer