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Luba_88 [7]
3 years ago
15

35 birds to 45 birds?

Mathematics
2 answers:
olya-2409 [2.1K]3 years ago
6 0
I'm not sure what your trying to ask is that the full question 

krok68 [10]3 years ago
3 0
There is a difference of 10
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In an election to the U.S. Senate, one candidate has popular support of 53% and the other has support of 47%. On election eve, a
Irina18 [472]

Answer:

a) 94.63% probability that the poll will predict the correct winner.

b) 69.15% probability of correct prediction. The lesser sample size leads to more variation, which means that the probability of correct prediction is smaller than in (a).

Step-by-step explanation:

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

\sqrt{V(X)} = \sqrt{np(1-p)}

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that \mu = E(X), \sigma = \sqrt{V(X)}.

(a) Compute a normal approximation with continuity correction of the probability that the poll will predict the correct winner.

The correct winner is the one with 53% of the votes.

We have that p = 0.53, n = 750.

So

E(X) = np = 750*0.53 = 397.5

\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{750*0.53*0.47} = 13.67

The pool will correctly predict the winner if the candidate that has a support of 53% gets more than half the votes.

So we have to find P(X > 750/2) = P(X > 375)[/tex]

Using continuity correction, this is P(X > 375 + 0.5) = P(X > 375.5), which is 1 subtracted by the pvalue of Z when X = 375.5. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{375.5 - 397.5}{13.67}

Z = -1.61

Z = -1.61 has a pvalue of 0.0537

1 - 0.0537 = 0.9463

94.63% probability that the poll will predict the correct winner.

(b) What happens to the probability of correct prediction if they had conducted the poll over only 100 voters?

Lesser sample size leads to more variation, which means that the probability of correct prediction will be smaller.

Now n = 100

Then

E(X) = np = 100*0.53 = 53

\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{100*0.53*0.47} = 4.99

Also P(X > 50), which using continuity correction is P(X > 50.5).

Z = \frac{X - \mu}{\sigma}

Z = \frac{50.5 - 53}{4.99}

Z = -0.5

Z = -0.5 has a pvalue of 0.3085

1 - 0.3085 = 0.6915.

69.15% probability of correct prediction. The lesser sample size leads to more variation, which means that the probability of correct prediction is smaller than in (a).

3 0
3 years ago
An advertising agency that serves a major radio station wants to estimate the mean amount of time the station’s audience members
Flura [38]

Answer:

n=(\frac{1.645(45)}{5})^2 =219.18 \approx 220

So the answer for this case would be n=220 rounded up to the nearest integer

Step-by-step explanation:

Information given

\sigma = 45 represent the population deviation

ME = 5 represent the margin of error

The margin of error for the true mean is given by this formula:

ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}    (a)

And on this case we have that ME =5 and we are interested in order to find the value of n, if we solve n from equation (4) we got:

n=(\frac{z_{\alpha/2} \sigma}{ME})^2   (b)

The critical value for 90% of confidence interval now can be founded using the normal distribution. The significance level is \alpha=1-0.9=0.1 and the critical value would be z_{\alpha/2}=1.645, replacing into formula (b) we got:

n=(\frac{1.645(45)}{5})^2 =219.18 \approx 220

So the answer for this case would be n=220 rounded up to the nearest integer

5 0
3 years ago
Read 2 more answers
Serial numbers for a product are to be made using 2 letters followed by 2 digits. The letters are to be taken from the first 6 l
Andru [333]
Alright so I'm coming up with this on the fly; you have the first six letters (a,b,c,d,e,f) and 0-9 and your ten numbers. calculate the amount of possible combinations for the letters by simply writing them down.
ab, ac, ad, ae, a f- five
bc, bd , be, bf- four
cd, ce, cf- three
de, df- two
ef,- one.
adding these all together gets a total of 15 for the letters. now the numbers
01, 02, 03, 04, 05, 06, 07, 08, 09- nine
12, 13, 14, 15, 16, 17, 18, 19- eight
23, 24, 25, 26, 27, 28, 29- seven
34, 35, 36, 37, 38, 39- six
45, 46, 47, 48, 49- five
56, 57, 58, 59- four
67, 68, 69- three
78, 79- two
89- one
added together with a total of 45 combinations.
alright so, 45 different number combinations and 15 letter combinations. multiplying 15 by 45 should tell you the total possible combinations for a two letter and two number serial-number

5 0
3 years ago
How do you write 6.359 × 10^-14 in standard form?
elixir [45]

6.359*10^-^1^4

Standard form:

-6.359*10^-^1^4

Since the exponent of the scientific notation is negative −14, move the decimal point 14 places to the left. 0.00000000000006359.

6 0
3 years ago
What is the successor of the natural number 2012?
andriy [413]
The succesor of the natural number 2012 is 2013.
4 0
3 years ago
Read 2 more answers
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