It is found that on average, 9% of the population recycles its garbage. Under this assumption, if a random sample of 120 households in Iowa City is taken, would you be surprised to find that fewer than 3% of households in the sample recycle their garbage? Use the fact that p-hat has an approximately normal distribution.

Group of answer choices

A I would not be surprised because there are lots of lazy students in Iowa City.

B I would not be surprised because 3% is not that far away from 9%.

C I would be surprised because Iowa City is a very clean community which means lots of people recycle their garbage.

D I would be surprised because if the 9% average is true, the chance of a sample proportion being less than 3% is very small (only 1%). Who cares? It's only garbage!

Answer:

The correct option is D

Step-by-step explanation:

From the question we are told that

The sample size is n = 120

The mean of the proportion is p = 0.09

Generally the standard deviation is mathematically represented as

$\sigma = \sqrt{\frac{p(1-p)}{n} }$

=> $\sigma = \sqrt{\frac{0.09(1-0.09)}{120 } }$

=> $\sigma = 0.02612$

Generally the chance that fewer than 3% of households in the sample recycle their garbage is mathematically represented as

$P(X < 0.03) = P( \frac{X - p}{\sigma} < \frac{0.03 -0.09}{0.02612} )$

$P(X < 0.03) = P( Z < -2.297 )$

From the z-table

$P( Z < -2.297 ) = 0.01$

=> [tex]P(X < 0.03) = 0.01/tex]

=> [tex]P(X < 0.03) = 1\% /tex]

4 0

3 years ago

I'm very confused on how to even figure out the question and what I'm supposed to do

Tasya [4]

Answer:

To solve a system of linear equations graphically we graph both equations in the same coordinate system. The solution to the system will be in the point where the two lines intersect. The two lines intersect in (-3, -4) which is the solution to this system of equations. I hope this helped!

5 0

2 years ago