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

4+  2 and 2+  2

Step-by-step explanation:

A rational number is a number that can be written as a ratio. That means it can be written as a fraction, in which both the numerator and the denominator are whole numbers.  

On the other hand, all numbers that are not rational are considered irrational. An irrational number can be written as a decimal, but not as a fraction.

So, let us take two irrational numbers a=4+  2  and b=2+ 2  and we now calculate a−b as follows:  a−b=(4+  2  )−(2+  2)=4+  2 −2−  2 =2=  1 2

​  

Therefore, the difference of two irrational numbers a and b is 2 and from the above defination of rational numbers, we get that 2 is a rational number.

Hence, the difference of two irrational numbers 4+  2 and 2+  2  is a rational number.