Coin tosses in a large class of introductory statistics students, the professor has each student toss a coin 16 times and calculate the proportion of his or her tosses that were heads. the students then report their results, and the professor plots a histogram of these several proportions. a. what shape would you expect this histogram to be? why? b. where do you expect the histogram to be centered? c. how much variability would you expect among these proportions? d. explain why a normal model should not be used here.

, 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