A hotel has 12 floors and 2,220 rooms. There are the same number of rooms on each floor of the hotel.

According to a Yale program on climate change communication survey, 71% of Americans think global warming is happening.† (a) For

SpyIntel [72]

Answer:

a) 0.2741 = 27.41% probability that at least 13 believe global warming is occurring

b) 0.7611 = 76.11% probability that at least 110 believe global warming is occurring

Step-by-step explanation:

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

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 $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

$p = 0.71$

(a) For a sample of 16 Americans, what is the probability that at least 13 believe global warming is occurring?

Here $n = 16$ , we want $P(X \geq 13)$ . So

$P(X \geq 13) = P(X = 13) + P(X = 14) + P(X = 15) + P(X = 16)$

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 13) = C_{16,13}.(0.71)^{13}.(0.29)^{3} = 0.1591$

$P(X = 14) = C_{16,14}.(0.71)^{14}.(0.29)^{2} = 0.0835$

$P(X = 15) = C_{16,15}.(0.71)^{15}.(0.29)^{1} = 0.0273$

$P(X = 16) = C_{16,16}.(0.71)^{16}.(0.29)^{0} = 0.0042$

$P(X \geq 13) = P(X = 13) + P(X = 14) + P(X = 15) + P(X = 16) = 0.1591 + 0.0835 + 0.0273 + 0.0042 = 0.2741$

0.2741 = 27.41% probability that at least 13 believe global warming is occurring

(b) For a sample of 160 Americans, what is the probability that at least 110 believe global warming is occurring?

Now $n = 160$ . So

$\mu = E(X) = np = 160*0.71 = 113.6$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{160*0.71*0.29} = 5.74$

Using continuity correction, this is $P(X \geq 110 - 0.5) = P(X \geq 109.5)$ , which is 1 subtracted by the pvalue of Z when X = 109.5. So

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

$Z = \frac{109.5 - 113.6}{5.74}$

$Z = -0.71$

$Z = -0.71$ has a pvalue of 0.2389

1 - 0.2389 = 0.7611

0.7611 = 76.11% probability that at least 110 believe global warming is occurring

3 0

2 years ago

3. Atile warehouse has Inventory at hand and can put in for a

Nookie1986 [14]

Step-by-step explanation:

Given the equation that represents this order expressed as;

The number of tiles = 12b + 38 where;

b is the the number of bundles ordered

If a customer needs 150 tiles, the total number of bundles ordered can be gotten by simply substituting The number of tiles into the modeled equation and find the value of b. This is as shown below;

On substituting;

150 = 12b + 38

12b = 150 - 38

12b = 112

b = 112/12

b = 9.33

b ≈ 9 bundles

We need to round up the problem because the number of tiles can not be in fraction but as whole numbers.

5 0

2 years ago

Alicia has 6 paintings she wants to hang side by side on her wall.

gayaneshka [121]

Answer:

A) 720 ways

B) 15 ways

C) 6 ways

Step-by-step explanation:

A) To find the number of ways Alicia can arranger her 6 paintings, we will find factorial of 6 by multiplying all of the positive integers equal to or less than that number i.e. 6 to get:

6! = 6 * 5 * 4 * 3 * 2 * 1 = 720

Alicia can arrange her paintings in 720 ways.

B) We use the following formula (when order is not important) to find the number of permutations of n objects taken r at a time:

$P(n, r) = \frac{n!}{r!(n-r)!}$

$= \frac{6!}{4!(6-4)!} = 15$

Therefore, Alicia can choose any 4 of her paintings in 15 ways.

C) Number of ways Alicia can arrange 3 out of 6 paintings = 3! = 3*2*1 = 6 ways

3 0

2 years ago

Goldilocks needs to find at least 12 lb of gold and at least 18 lb of silver to pay the monthly rent. There are two mines in whi

VikaD [51]

Answer:

cave 1 - 2g= 12 gold, g is 6

2s = 18 silver, s = 9

so she would stay 9 days digging for silver and 6 for gold

cave 2- 1g = 12 gold, g is 12

3s = 18 silver, s = 4

she would stay 4 days looking for silver and 12 for gold

cave 1 is better because its less days since she is digging for gold and silver at same time it would only take maybe 10 days but for cave 2 its would take abt 13 days

Step-by-step explanation: idk i just put some stuff together sorrry its wrong..... but i hope it helps..

6 0

2 years ago

Four research teams each used a different method to collect data on how fast a new strain of maize sprouts. Assume that they all

Westkost [7]

Confidence Level: 95%; Confidence Interval: 44 to 46

5 0

2 years ago

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