Question

Monthly Mortgage Payments The average monthly mortgage payment including principal and interest is $982 in the United States. Assume that the standard

deviation is approximately $180 and the mortgage payments are approximately normally distributed. Find these probabilities of the monthly payment selected
randomly. Enter the final answers as decimals rounded to at least four places. Round intermediate z-value calculations to two decimal places.
Part 1 of 2
(a) More than $1430
P(X> 1430)= 0.0179
Correct Answer:
P(X> 1430) 0.0064
A
Part: 1/2
Part 2 of 2
=
(b) Between $720 and $1230
P(720

Answer 1

The selected monthly payment is more than More than
`\( P(X > 1430) \approx 0.0034 \)`.

The selected monthly payment is between
`\( P(720 < X < 1230) \approx 0.8862 \)`.

Let's use the z-score formula to find the probabilities for the given mortgage payments.

The z-score formula is given by:

`\[ z = \frac{{X - \mu}}{{\sigma}} \]`

where:

-
`\( X \)` is the mortgage payment,

-
`\( \mu \)` is the mean mortgage payment,

-
`\( \sigma \)` is the standard deviation.

Given:

- Mean
`(\( \mu \))` = $982,

- Standard Deviation
`(\( \sigma \))` = $180.

Part 1: More than $1430

`\[ z = \frac{{1430 - 982}}{{180}} \]`

`\[ z \approx 2.7111 \]`

Now, we look up the z-score of 2.71 in the z-table. The probability of
`\( X > 1430 \)` is the area to the right of this z-score.

The correct answer is
`\( P(X > 1430) \approx 0.0034 \)` (rounded to four decimal places).

Part 2: Between $720 and $1230

For
`\( X = 720 \)`:

`\[ z_(720) = \frac{{720 - 982}}{{180}} \]`

`\[ z_(720) \approx -1.4556 \]`

For X = 1230:

`\[ z_(1230) = \frac{{1230 - 982}}{{180}} \]`

`\[ z_(1230) \approx 1.3833 \]`

Now, we look up these z-scores in the z-table. The probability of
`\( 720 < X < 1230 \)` is the area between these z-scores.

`\[ P(720 < X < 1230) = P(z_(720) < z < z_(1230)) \]`

The correct answer for
`\( P(720 < X < 1230) \)` is approximately 0.8862 (rounded to four decimal places).

So, the corrected answers are:

(a)
`\( P(X > 1430) \approx 0.0034 \)`

(b)
`\( P(720 < X < 1230) \approx 0.8862 \)`

Complete question:

Monthly Mortgage Payments The average monthly mortgage payment including principal and interest is $982 in the United States. Assume that the standard deviation is approximately $180 and the mortgage payments are approximately normally distributed. Find these probabilities of the monthly payment selected randomly. Enter the final answers as decimals rounded to at least four places. Round intermediate z-value calculations to two decimal places.

Part 1 of 2

(a) The selected monthly payment is more than More than $1430

Part 2 of 2

(b) The selected monthly payment is between $720 and $1230