A sample survey contacted an SRS of 2854 registered voters shortly before the 2012 presidential election and asked respondents whom they planned to vote for. Election results show that 51% of registered voters voted for Barack Obama. We will see later that in this situation the proportion of the sample who planned to vote for Barack Obama (call this proportion V) has approximately the Normal distribution with mean μ 0.52 and standard deviation σ = 0.009. (a) If the respondents answer truthfully, what is P (0.5くV < 0.54)? This is the probability that the sample proportion v estimates the population proportion 0.52 within plus or minus 0.02.
P (0.5<= V <=0.54) (±0.0001)=

(b) In fact, 50% of the respondents said they planned to vote for Barack Obama V = 0.5. If respondents answer truthfully, What is P(V <=0.5)?
P (V <=0.5) (±0.0001) =

Answers

Answer 1
Answer:

Answer:

a) 97.37%

b) 1.31%

Step-by-step explanation:

a)  

Here we want to calculate the area under the Normal curve with mean 0.52 and standard deviation 0.009 between 0.5 and 0.54

This can be easily done with a spreadsheet and we get

P (0.5くV < 0.54) = 0.9737 or 97.37%

(See picture 1)

b)

Here we want the area under the Normal curve with mean 0.52 and standard deviation 0.009 to the left of 0.5.

P(V ≤ 0.5) = 0.0131 or 1.31%

(See picture 2)


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Use the following results from a test for marijuana use, which is provided by a certain drug testing company. Among 147 subjects with positive test results, there are 30 false positive results; among 157 negative results, there are 4 false negative results. If one of the test subjects is randomly selected, find the probability that the subject tested negative or did not use marijuana. (Hint: Construct a table.)a. The probability that a randomly selected subject tested negative or did not use marijuana is___________.
(Do not round until the final answer. Then round to three decimal places as? needed.)
b. How many subjects were included in the study?
The total number of subjects in the study was___.
c. How many subjects did not use marijuana?
A total of ___subjects did not use marijuana.

Answers

Answer:

(a)0.615

(b)304

(c)183

Step-by-step explanation:

Among 147 subjects with positive test results, there are 30 false positive (actually negative) results;

Among 157 negative results, there are 4 false-negative (actual positive) results.

The table below summarises the given data.

\left\begin{array}{c|c|c|cc}&$Use Marijuana&$Did Not Use Marijuana&$Total\n---&-------&-------&-------\n$Positive Result&117&30&147\n$Negative Result&4&153&157\n---&-------&-------&-------\n$Total&121&183&304\end{array}\right

(a)The probability that a randomly selected subject tested negative or did not use marijuana

P(negative or did not use marijuana)

=P(negative)+P(did not use marijuana)-P(both)

=(157)/(304)+ (183)/(304)-(153)/(304)\n=(187)/(304)\n\n\approx 0.615

(b)There were a total of 304 subjects in the study.

(c)A total of 183 subjects did not use marijuana.

A large operator of timeshare complexes requires anyone interested in making a purchase to first visit the site of interest. Historical data indicates that 20% of all potential purchasers select a day visit, 50% choose a one-night visit, and 30% opt for a two-night visit. In addition, 10% of day visitors ultimately make a purchase, 30% of onenight visitors buy a unit, and 20% of those visiting for two nights decide to buy. Suppose a visitor is randomly selected and is found to have made a purchase. How likely is it that this person made a day visit? A one-night visit? A two-night visit?

Answers

Answer:

0.087 = 8.7% probability that this person made a day visit.

0.652 = 65.2% probability that this person made a one-night visit.

0.261 = 26.1% probability that this person made a two-night visit.

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

P(B|A) = (P(A \cap B))/(P(A))

In which

P(B|A) is the probability of event B happening, given that A happened.

P(A \cap B) is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Made a purchase.

Probability of making a purchase:

10% of 20%(day visit)

30% of 50%(one night)

20% of 30%(two night).

So

p = 0.1*0.2 + 0.3*0.5 + 0.2*0.3 = 0.23

How likely is it that this person made a day visit?

Here event B is a day visit.

10% of 20% is the percentage of purchases and day visit. So

P(A \cap B) = 0.1*0.2 = 0.02

So

P(B|A) = (P(A \cap B))/(P(A)) = (0.02)/(0.23) = 0.087

0.087 = 8.7% probability that this person made a day visit.

A one-night visit?

Event B is a one night visit.

The percentage of both(one night visit and purchase) is 30% of 50%. So

P(A \cap B) = 0.3*0.5 = 0.15

So

P(B|A) = (P(A \cap B))/(P(A)) = (0.15)/(0.23) = 0.652

0.652 = 65.2% probability that this person made a one-night visit.

A two-night visit?

Event B is a two night visit.

The percentage of both(two night visit and purchase) is 20% of 30%. So

P(A \cap B) = 0.2*0.3 = 0.06

Then

P(B|A) = (P(A \cap B))/(P(A)) = (0.06)/(0.23) = 0.261

0.261 = 26.1% probability that this person made a two-night visit.

A total of 634 tickets were sold for the school play. They were either adult tickets or student tickets. There were 66 fewer students tickets sold than adult tickets. Him many adult tickets were sold?

Answers

 A total of 634 tickets were sold for the school play. They were either adult tickets or student tickets. There were 66 fewer student tickets sold than adult tickets. How many adult tickets were sold?
So say adult sold would be x, then student sold would be x-66
add them

x+x-66=634 solve for x
2x=700 divide each side by 2
x=350
so 350 adult and 350-66=284 student
x= student tickets
y= adult tickets 

x+y=634
y=x-66

x+y=634 x-y=66   2x=700 x=350 

350+y=634  y=284

An above-ground swimming pool in the shape of a cylinder has a diameter of 16 feet and a height of 5 feet. If the pool is filled with water to 1.5 inches from the top of the pool, what is the volume, to the nearest cubic foot, of the water in the pool?⇆

Answers

Answer is lots of god Which equation is the inverse of y = 100 – x2?

Find the solution(s) to the system of equations. Select all that apply.y = x^2-2x-3
y=2x-3

Answers

Answer:

(0, -3) and (4, 5)

Step-by-step explanation:

y = x² − 2x − 3

y = 2x − 3

2x − 3 = x² − 2x − 3

0 = x² − 4x

0 = x (x − 4)

x = 0 or 4

What is the absolute value of -3

Answers

3
it’s just how far away that number is from zero