Na survey of 1227 people, 828 people said they voted in a recent presidential election. voting records show that 65% of eligible voters actually did vote. given that 65% of eligible voters actually did vote. a) find the probability that among 1227 randomly selected voters, at least 828 actually did vote. b) what do the results from part (a) suggest?

0.0344

Step-by-step explanation:

For binomial distribution :-

, where p is the proportion of success in each trial and n is the sample size.

Given : Sample size : n=1227

The proportion of people said they voted in a recent presidential election :p=0.95

Then,

Let X be the binomial variable.

z-score :

For x= 828

Then,  probability that among 1227 randomly selected voters, at least 828 actually did vote is given by :-

Hence,  the probability that among 1227 randomly selected voters, at least 828 actually did vote= 0.0344

step-by-step explanation: h: (- 3, 6)

m: (1, - 2)

o: (7, 6)

r: (- 9, - 2)

midpoint of hm: (- 1, 2)

midpoint of or: (- 1, 2)

therefore, b is the midpoint of both diagonals bisect each other !

to prove the diagonals are perpendicular, show that the product of the slopes = - 1