Longest Day, June 20th 2021: 14.93 daylight hours Shortest Day, December 21st 2020: 9.30 daylight hours

Hint: You will need to find the amplitude, vertical shift (midline), and "b" from the period in order to solve this problem.

Question 1
What is the average number of summer hours per day (the midline) for the function?
A. 12.12
B. 24
C. 10.47
D. 11.87

Question 2
What is the amplitude of the function for the number of daylight hours?
A. 2.015
B. 2.995
C. 2.375
D. 2.82

Question 3
What is the period for this function?
A. 91 days
B. 180 days
C. 720 days
D. 365 days

Question 4
Which trig function did you use to model it?
A. -cos
B. cos
C. -sin
D. sin

Question 5
Choose the right function, assuming your function will start at winter solstice in 2020. Pick the one that is closest.
A. =−2.995cos(365())+14.945
B. =−2.375cos(2365())+18.155
C. =−2.816cos(2365())+12.117
D. =−2.015cos(365())+12.175

How many hours of daylight will there be on May 28, 2021?

How many hours of daylight will there be on August 15, 2021?

How many hours of daylight will there be on November 15, 2021?

Step-by-step explanation:

k

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: