Binomial, Normal distrib.: 20 voters polled in large city re: mayoral candidate

Akira

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Aug 10, 2016
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1
1) Suppose a poll of 20 voters is taken in a large city. The purpose is to determine the numbers who favor a certain candidate for mayor. Suppose that 60% of all the city’s voters favor the candidate.
Find the following:
i. Find the mean and standard deviation of x. Answer: mean=12 and standard deviation=2.19
ii. Find the probability that x<=10 Answer: 0.245
iii. Find the probability that x>12. Answer: 0.416
iv. Find the probability that x=10. Answer: 0.159

I assumed that by x the question means the number of voters. I'm not sure how to get the answer for ii, iii and iv. I used the nCxp^xq^(n-x) formula but maybe I'm taking the wrong values for n and x. Can someone explain the correct way to work-out ii-iv ?


2)
The grade - point average score of 80 student of Department of Computer Science of Dhaka University in their term final examination was found to follow approximately a normal distribution with a mean of 2.1 and a standard deviation 0.6. How many of the students are expected to have a score between 2.5 and 3.5? (Answer: 20)

As for this one, I've no clue how to find the number of students- I found all the z-values and all but how will that help me to to find the numberof students expected to have a score between 2.5 and 3.5? What's the work-out for this one?
 
1) Suppose a poll of 20 voters is taken in a large city. The purpose is to determine the numbers who favor a certain candidate for mayor. Suppose that 60% of all the city’s voters favor the candidate.
Find the following:
i. Find the mean and standard deviation of x. Answer: mean=12 and standard deviation=2.19
ii. Find the probability that x<=10 Answer: 0.245
iii. Find the probability that x>12. Answer: 0.416
iv. Find the probability that x=10. Answer: 0.159

I assumed that by x the question means the number of voters. I'm not sure how to get the answer for ii, iii and iv. I used the nCxp^xq^(n-x) formula but maybe I'm taking the wrong values for n and x. Can someone explain the correct way to work-out ii-iv ?

You are using the correct formula.
First of all, what values are you using for n, p and x for each question?
(Also, I disagree with the answer for (iv). Please check the question and answer you've given.)



2)
The grade - point average score of 80 student of Department of Computer Science of Dhaka University in their term final examination was found to follow approximately a normal distribution with a mean of 2.1 and a standard deviation 0.6. How many of the students are expected to have a score between 2.5 and 3.5? (Answer: 20)

As for this one, I've no clue how to find the number of students- I found all the z-values and all but how will that help me to to find the numberof students expected to have a score between 2.5 and 3.5? What's the work-out for this one?

What are the z-values you have found?

Draw a bell-shaped curve and shade in the relevant area.

You then find the probability (area under the normal curve) between them.

Then take into account that you have 80 students. eg If the prob =0.4 then you would expect 0.4x80=32 students out of 80 to have scores between...
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