Mathematics, 09.01.2020 00:31 valdezavery9018

About 11% of adult americans are left-handed. suppose that two people are randomly selected from this
population.
a. create a discrete probability distribution for the number of left-handed people in a sample of two randomly
selected adult americans.
b. what is the probability that at least one person in the sample is left-handed?

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Answer from: xonyemaa12

a) $P(X=0)=(2C0)(0.11)^0 (1-0.11)^{2-0}=0.7921$

$P(X=1)=(2C1)(0.11)^1 (1-0.11)^{2-1}=0.1958$

$P(X=2)=(2C2)(0.11)^2 (1-0.11)^{2-2}=0.0121$

And then we have our probability distribution like this:

X | 0 | 1 | 2 |

P(X) | 0.7921 | 0.1958 | 0.0121|

b) $P(X \geq 1) = P(X=1)+P(X=2) = 0.1958+0.0121=0.2079$

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=20, p=0.48)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

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

Solution for the problem

Part a

On this case since we select a sample size of n =2 we have the following values for the number of left handed X=0,1,2. We can find the probabilities for each case since we know that p=0.11.

$P(X=0)=(2C0)(0.11)^0 (1-0.11)^{2-0}=0.7921$

$P(X=1)=(2C1)(0.11)^1 (1-0.11)^{2-1}=0.1958$

$P(X=2)=(2C2)(0.11)^2 (1-0.11)^{2-2}=0.0121$

And then we have our probability distribution like this:

X | 0 | 1 | 2 |

P(X) | 0.7921 | 0.1958 | 0.0121|

Part b

For this case we want this probability:

$P(X \geq 1) = P(X=1)+P(X=2) = 0.1958+0.0121=0.2079$

Answer from: Quest

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200. after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes 1800 - 6400 which gets you 11,600.

Answer from: Quest

12cm

the answer is d

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