The time X it takes Professor Sawyer to drive to campus on a randomly selected day follows a distribution that is approximately Normal with mean 37 minutes and standard deviation 3 minutes. After parking his car it takes an additional 3 minutes to walk to his classroom and 2 minutes to start the computer. Then he is ready to begin class. Let T = the total time it takes Professor Sawyer to get to his classroom and be ready to begin class. Describe the shape, center, and variability of the probability distribution of T.

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step-by-step explanation:

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for