Question

6. In 1974, then president Richard Nixon had an approval rating of 24% (so, 24% of the U.S. population approved of his work as president).

(a) Suppose the Nixon administration claimed to have polled 100% U.S. citizens at random and claims that 68 of them approved of Nixon. How likely is this claim? (that is, determine the probability of this actually happening given that the true approval rating is 24%....)

(b) Suppose that a news program wants to collect viewpoints of U.S. citizens on Nixon. What is the minimum number of viewpoints they must collect in order to get at least two perspectives supportive of Nixon?

7. If a reservations calling center for a major airline on average receives 8 calls per minute, what is the probability of getting less than 2 calls per minute?

8. Suppose that, on average, 1 in 100 people make an error preparing their tax return when filing an electronic return. If 1000 return is selected, what is the probability that less than 5 returns have errors?

Answer 1

6. (a) Let X denote the number of approval out of 100 random people then X follows Binomial with parameter (100, 0.24).

Then P(X=64) =2.182028e-17 which is approximately equal to zero.

(b). Here let Y denote the number of Viewpoints required to have two perspectives supportive of Nixon then Y follows Negative binomial with parameter (2 , 0.24). Hence, E(Y) = 2/0.24 = 8.333 i.e. they need at least 9 viewpoints.

7. Let X denote the number of calls per minute then X follow s Poisson with parameter 8. Hence P(X<2) =0.003

8. Let Y denote the number of errors from the 1000 return selected the Y follows Binomial(1000, 0.01). Then P(Y<5) = 0.0287

Here I'm also attaching the R code: