Question

1. Suppose that 16% of students at PCU (a large university) believe that the entire campus should be a safe zone in which no one can say anything that offends anyone. That is, students either favor safe zone or do not favor safe zone.

a. In a sample of size 120 what is the probability that more than 20% favor the safe zone?

i. Answer the question using the normal approximation for the distribution of pHAT using each of the following methods.

1. Answer using EXCEL Norm.dist

2. Answer using the z table in your text.

ii. Answer the question using the Binom.Dist EXCEL function.

iii. Using the simulation data in Simulation Mean. Xlsx on the worksheet sim PHAT estimate the answer based on the 500 simulated pHAT values.

2. Suppose that the average bill for repairs from an auto accident is $1200 with standard deviation $5000.

a.Do you think that the repair bills follow the normal distribution? Explain.

b. In a sample of 90 bills find the probability that the average bill is less than $2000.

i. Answer using the norm.dist function.

ii. Answer using the z table in your book.

Answer 1

1(a)

Here we have

(1)

The sampling distribution of sample proprotion will be approximately normal with mean

and standard deviation

(1)

We need to find the probability that more than 20% favor the safe zone that is we need to find :

Using excel function "=1-NORMDIST(0.2,0.16,0.0335,TRUE)" is

(2)

The z-score for is

The probability that more than 20% favor the safe zone is

(ii)

20% of 120 means 120*0.20 = 24.

Using binomial function "=1-BINOMDIST(24,120,0.16,TRUE)" the required probability is;

(iii)

For this part we need excel file as menioned.