Garrett and erin are borrowing $170,000 to purchase a new home. they have been approved for a 30-year loan with an interest rate of 5.75%. what will be their monthly payment?

Step-by-step explanation:

Since, the periodic payment of a loan,

Where, P.V. is the principal amount,

r is the rate per period,

n is the number of periods,

Given,

P.V. = $ 170,000,

Annual rate = 5.75 % = 0.0575,

Thus, the rate per month,

Also, time = 30 years,

So, the number of months in 30 years,

n = 360   ( 1 year =12 months )

Hence, the monthly payment of the loan is,

a) What is the probability that the duration of a particular rainfall event at this location is at least 2 hours?

We want this probability"

At most 3 hours?

b) What is the probability that rainfall duration exceeds the mean value by more than 2 standard deviations?

What is the probability that it is less than the mean value by more than one standard deviation?

Step-by-step explanation:

Previous concepts

The exponential distribution is "the probability distribution of the time between events in a Poisson process (a process in which events occur continuously and independently at a constant average rate). It is a particular case of the gamma distribution". The probability density function is given by:

The cumulative distribution for this function is given by:

We know the value for the mean on this case we have that :

Solution to the problem

Part a

What is the probability that the duration of a particular rainfall event at this location is at least 2 hours?

We want this probability"

At most 3 hours?

Part b

What is the probability that rainfall duration exceeds the mean value by more than 2 standard deviations?

The variance for the esponential distribution is given by:

And the deviation would be:

And the mean is given by

Two deviations correspond to 5.540, so we want this probability:

What is the probability that it is less than the mean value by more than one standard deviation?

For this case we want this probablity: