Can you help me with these 2 questions?
1 answer:
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Complete Question
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
=>
=>
Generally the chance that fewer than 3% of households in the sample recycle their garbage is mathematically represented as
From the z-table
=> [tex]P(X < 0.03) = 0.01/tex]
=> [tex]P(X < 0.03) = 1\% /tex]
To solve this we will divide the given composite figure into three figures. The three figures will be 2 squares and 1 rectangle. Let's find their areas and add them!
- Side 3 metre
<em>Thus, The area of 1st square is 9m²...</em>
- The area of second square will be also 9m², because the sides of both squares are equal.
- Length = 6m
- Breadth = 7+3=10m
<em>Thus, The area of rectangle is 30m²....</em>
- Now, Add area of all the figures to get the total area.