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Kobotan [32]
3 years ago
14

List the probability value for each possibility in the binomial experiment calculated at the beginning of this lab, which was ca

lculated with the probability of a success being ½. (Complete sentence not necessary; round your answers to three decimal places)P(x=0) P(x=6)
P(x=1) P(x=7)
P(x=2) P(x=8)
P(x=3) P(x=9)
P(x=4) P(x=10)
P(x=5)
Mathematics
1 answer:
Yanka [14]3 years ago
4 0

Answer:

a. P(X = 0)= 0.001

b. P(X = 1)= 0.001

c. P(X=2)= 0.044

d. P(X=3)= 0.117

e. P(X=4)= 0.205

f. P(X=5)= 0.246

g. P(X=6)= 0.205

h. P(X=7)= 0.117

i. P(X=8)= 0.044

j. P(X=9)= 0.001

k. P(X=10)= 0.001

Step-by-step explanation:

Hello!

You have the variable X with binomial distribution, the probability of success is 0.5 and the sample size is n= 10 (I suppose)

If the probability of success p=0.5 then the probability of failure is q= 1 - p= 1 - 0.5 ⇒ q= 0.5

You are asked to calculate the probabilities for each observed value of the variable. In this case is a discrete variable with definition between 0 and 10.

You have two ways of solving this excersice

1) Using the formula

P(X)= \frac{n!}{(n-X)!X!} * (p)^X * (q)^{n-X}

2) Using a table of cummulative probabilities of the binomial distribution.

a. P(X = 0)

Formula:

P(X=0)= \frac{10!}{(10-0)!0!} * (0.5)^0 * (0.5)^{10-0}

P(X = 0) = 0.00097 ≅ 0.001

Using the table:

P(X = 0) = P(X ≤ 0) = 0.0010

b. P(X = 1)

Formula

P(X=1)= \frac{10!}{(10-1)!1!} * (0.5)^1 * (0.5)^{10-1}

P(X = 1) = 0.0097 ≅ 0.001

Using table:

P(X = 1) = P(X ≤ 1) - P(X ≤ 0) = 0.0107-0.0010= 0.0097 ≅ 0.001

c. P(X=2)

Formula

P(X=2)= \frac{10!}{(10-2)!2!} * (0.5)^2 * (0.5)^{10-2}

P(X = 2) = 0.0439 ≅ 0.044

Using table:

P(X = 2) = P(X ≤ 2) - P(X ≤ 1) = 0.0547 - 0.0107= 0.044

d. P(X = 3)

Formula

P(X = 3)= \frac{10!}{(10-3)!3!} * (0.5)^3 * (0.5)^{10-3}

P(X = 3)= 0.11718 ≅ 0.1172

Using table:

P(X = 3) = P(X ≤ 3) - P(X ≤ 2) = 0.1719 - 0.0547= 0.1172

e. P(X = 4)

Formula

P(X = 4)= \frac{10!}{(10-4)!4!} * (0.5)^4 * (0.5)^{10-4}

P(X = 4)= 0.2051

Using table:

P(X = 4) = P(X ≤ 4) - P(X ≤ 3) = 0.3770 - 0.1719= 0.2051

f. P(X = 5)

Formula

P(X = 5)= \frac{10!}{(10-5)!5!} * (0.5)^5 * (0.5)^{10-5}

P(X = 5)= 0.2461 ≅ 0.246

Using table:

P(X = 5) = P(X ≤ 5) - P(X ≤ 4) = 0.6230 - 0.3770= 0.246

g. P(X = 6)

Formula

P(X = 6)= \frac{10!}{(10-6)!6!} * (0.5)^6 * (0.5)^{10-6}

P(X = 6)= 0.2051

Using table:

P(X = 6) = P(X ≤ 6) - P(X ≤ 5) = 0.8281 - 0.6230 = 0.2051

h. P(X = 7)

Formula

P(X = 7)= \frac{10!}{(10-7)!7!} * (0.5)^7 * (0.5)^{10-7}

P(X = 7)= 0.11718 ≅ 0.1172

Using table:

P(X = 7) = P(X ≤ 7) - P(X ≤ 6) = 0.9453 - 0.8281= 0.1172

i. P(X = 8)

Formula

P(X = 8)= \frac{10!}{(10-8)!8!} * (0.5)^8 * (0.5)^{10-8}

P(X = 8)= 0.0437 ≅ 0.044

Using table:

P(X = 8) = P(X ≤ 8) - P(X ≤ 7) = 0.9893 - 0.9453= 0.044

j. P(X = 9)

Formula

P(X = 9)= \frac{10!}{(10-9)!9!} * (0.5)^9 * (0.5)^{10-9}

P(X = 9)=0.0097 ≅ 0.001

Using table:

P(X = 9) = P(X ≤ 9) - P(X ≤ 8) = 0.999 - 0.9893= 0.001

k. P(X = 10)

Formula

P(X = 10)= \frac{10!}{(10-10)!10!} * (0.5)^{10} * (0.5)^{10-10}

P(X = 10)= 0.00097 ≅ 0.001

Using table:

P(X = 10) = P(X ≤ 10) - P(X ≤ 9) = 1 - 0.9990= 0.001

Note: since 10 is the max number this variable can take, the cummulated probability until it is 1.

I hope it helps!

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in the unted states, the height of men are normally distributed with the mean 69 inches and standard deviation 2.8 inches. If 16
yaroslaw [1]

Answer:

Probability that their mean height is less than 68 inches is 0.0764.

Step-by-step explanation:

We are given that in the united states, the height of men are normally distributed with the mean 69 inches and standard deviation 2.8 inches.

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The z-score probability distribution for sample mean is given by;

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The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) 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.

So, probability that the mean height of 16 randomly selected men is less than 68 inches is given by = P(\bar X < 68 inches)

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Karo-lina-s [1.5K]

She has 45% of the original amount left

<h3>Ratio and proportions</h3>

Fractions are written as a ratio of two integers

Given the following

Initial amount. = ∈4000


Amount given to her sister = 1/4 * 4000 = 1000

Amount given to her brother = 40% of 3000 = 1200

Amount left = 4000 - (1000+1200)

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Determine the percentage left

x * 4000 = 1800

x = 1800/4000

x = 0.45

x = 45%

Hence she has 45% of the original amount left

Learn more proportion here: brainly.com/question/19994681

#SPJ1

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