Question

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.

(a)

(a)The selected monthly payment is more than

$1400

(a)The selected monthly payment is more than 1400

P(Z>1400)=

2) Prison Sentences The average prison sentence for a person convicted of second-degree murder is 16 years.

If the sentences are normally distributed with a standard deviation of 1.8 years, find the following probabilities. round to four decimal places.

A prison sentence is greater than 19 years.

P(X>19)=

I can't find the answer because I don't think I have the right calculator. Please help.

Answer 1

This is a normal distribution question with

a P(x > 1400.0)=?
The z-score at x = 1400.0 is,

z = 2.3222
This implies that
P(x > 1400.0) = P(z > 2.3222) = 1 - 0.9898889155016486

PS: you have to refer z score table to find the final probabilities.
To solve it with TI-84
Step 1. Press 2nd button
Step 2. Press VARS button
Step 3. choose normal cdf
Step 4. enter normalcdf(1400, 100000000, 982, 180)

This is a normal distribution question with

P(x > 19.0)=?
The z-score at x = 19.0 is,

z = 1.6667
This implies that
P(x > 19.0) = P(z > 1.6667) = 1 - 0.9522129635397043

PS: you have to refer z score table to find the final probabilities.
To solve it with TI-84
Step 1. Press 2nd button
Step 2. Press VARS button
Step 3. choose normal cdf
Step 4. enter normalcdf(19, 100000000, 16, 1.8)
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