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3 years ago

If you flip a coin 4 times, what is the best prediction possible for the number of times it will land on tails?

Mathematics

1 answer:

allochka39001 [22]3 years ago

7 0

Answer:

Step-by-step explanation:

Each time you flip a coin, there is a 50% change of it landing on tails. So half the time you should get a tails.

Half of 4 is 2, so you will likely get 2 tails.

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A public health organization reports that 40%of baby boys 6-8 months old in the United

Sveta_85 [38]

Using the binomial distribution, the probabilities are given as follows:

0.3675 = 36.75% probability that more than 4 weigh more than 20 pounds.

0.1673 = 16.73% probability that fewer than 3 weigh more than 20 pounds.

Since P(X > 7) < 0.05, it would be unusual if more than 7 of them weigh more than 20 pounds.

<h3>What is the binomial distribution formula?</h3>

The formula is:

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

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

The parameters are:

x is the number of successes.

n is the number of trials.

p is the probability of a success on a single trial.

The values of the parameters for this problem are:

n = 10, p = 0.4.

The probability that more than 4 weigh more than 20 pounds is:

$P(X > 4) = 1 - P(X \leq 4)$

In which:

$P(X \leq 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)$

Then:

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

$P(X = 0) = C_{10,0}.(0.4)^{0}.(0.6)^{10} = 0.0061$

$P(X = 1) = C_{10,1}.(0.4)^{1}.(0.6)^{9} = 0.0403$

$P(X = 2) = C_{10,2}.(0.4)^{2}.(0.6)^{8} = 0.1209$

$P(X = 3) = C_{10,3}.(0.4)^{3}.(0.6)^{7} = 0.2150$

$P(X = 4) = C_{10,4}.(0.4)^{4}.(0.6)^{6} = 0.2502$

Hence:

$P(X \leq 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.0061 + 0.0403 + 0.1209 + 0.2150 + 0.2502 = 0.6325$

$P(X > 4) = 1 - P(X \leq 4) = 1 - 0.6325 = 0.3675$

0.3675 = 36.75% probability that more than 4 weigh more than 20 pounds.

The probability that fewer than 3 weigh more than 20 pounds is:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0061 + 0.0403 + 0.1209 = 0.1673

0.1673 = 16.73% probability that fewer than 3 weigh more than 20 pounds.

For more than 7, the probability is:

$P(X > 7) = P(X = 8) + P(X = 9) + P(X = 10)$

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

$P(X = 8) = C_{10,8}.(0.4)^{8}.(0.6)^{2} = 0.0106$

$P(X = 9) = C_{10,9}.(0.4)^{9}.(0.6)^{1} = 0.0016$

$P(X = 10) = C_{10,10}.(0.4)^{10}.(0.6)^{0} = 0.0001$

Since P(X > 7) < 0.05, it would be unusual if more than 7 of them weigh more than 20 pounds.

More can be learned about the binomial distribution at brainly.com/question/24863377

#SPJ1

4 0

2 years ago

Can someone help me with this? 8th grade math

tatyana61 [14]

Answer:

ooohh yeah i kinda suck at geometry lol nearly failed sophomore year last year haha

Step-by-step explanation:

6 0

3 years ago

14.4% of what number is 10.4

Helga [31]

First, convert "of" to x and put this info into an equation:

Let n represent the unknown number.

14.4 % x n= 10.4
n = 10.4 / 14.4%
n = 72.22222
n = ~72

Hope this helps!

8 0

4 years ago

(x-5)1/2+5=2<br> (x-5)1/2=-3<br> [(x-5)^1/2]^2=(-3)^2

Studentka2010 [4]

Answer:

x = 14

Step-by-step explanation:

You want to solve for x, right?

(x-5)^(1/2)+5=2

You have it right so far.

(x - 5)^(1/2) = -3

(x - 5) = (-3)^2

x - 5 = 9

x = 9 + 5 = 14

3 0

3 years ago

There are about 6,600,000,000 people living in the world. the male to female ratio is 107 to 100. about how many males are there

seropon [69]

3,300,000,000 would be you answer so A.

8 0

3 years ago

Read 2 more answers