X squared +20 equals 2X

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

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4 0

2 years ago

The vertex of this parabola is (2,-1). When the y value is 0, the x value is 5. What is the coefficient of the squared term in t

Schach [20]

Vertex form: y = a(x - h)² + k
h = 2
k = -1
y = 0
x = 5

0 = a(5 - 2)² - 1
0 = 9a - 1
a = 1/9

5 0

3 years ago

x= infinity; 9x to the power of 3 + x to the power of 2 - 5 divided by 3x to the power of 4 + 4x to the power of 2

Delvig [45]

Answer:

here n Hope it helps. goodluck

5 0

2 years ago

The _____ in the hundreds place has a value ____ times as great as the _____ in the _____ place. 440

solong [7]

Answer:

The 4 in the hundreds place has a value 10 times as great as the 4 in the tens place.

Step-by-step explanation:

440 = 400 + 40 + 0

the hundreds place is worth 400 here

it is worth 10x the tens place (40 here)

5 0

3 years ago

My brother is in 6th grade and needs help with his math. I tried to help but I can't find any answers on it.

In-s [12.5K]

Answer:

Question 1) 17.4

Question 2) 1.7

Question 3) 2.8

Question 4) 8.6

Step-by-step explanation:

Mean absolute deviation is the average distance between the data points from the set to the mean point of the data set. It shows the variability in data or how much the data points are spread.

method to calculate Mean absolute deviation:

a. calculate mean

b. calculate absolute deviation of each data point

c. add all the deviations

d. divide absolute deviation by number of points

mean absolute deviation = ∑l $x_{i}$ -xl / n

The given problem has four sub-parts

Solution 1:

Mean= (78+99+90+80+55+56+102+88+60+42)/10

= 750/10

= 75

Mean absolute deviation= ( I 78-75 I + I 99-75 I+I 90-75 I + I 80-75 I +

I 55-75 I + I 56-75 I + I 102-75 I + I 88- 75 I +

I 60-75 I + I 42-75 I) /10

= (174)/10

= 17.4

Solution 2:

Mean = (10+13+7+12+9+8+12+10+11+13)/10

= (105)/10

= 10.5

Mean absolute deviation = ( I 10-10.5 I + I 13-10.5 I + I 7-10.5 I + I 12-10.5 I +

I 9-10.5 I + I 8-10.5 I + I 12-10.5 I + I 10-10.5 I +

I 11-10.5 I + I 3-10.5 I) /10

= 17/10

= 1.7

Solution 3:

Mean= (1+7+10+5+3+3+6+12+9+4)/10

= 60/10

= 6

Mean absolute deviation = ( I 1-6 I + I 7-6 I + I 10-6 I + I 5-6 I + I 3-6 I +

I 3-6 I + I 6-6 I + I 12- 6 I + I 9-6 I + I 4-6 I) /10

= (28)/10

= 2.8

Solution 4:

Mean= (30+46+25+45+18+25+15+32+40+24)/10

= 300/10

= 30

Mean absolute deviation = ( I 30-30 I + I 46-30 I + I 25-30 I + I 45-30 I +

I 18-30 I + I 25-30 I + I 15-30 I + I 32-30 I +

I 40-30 I + I 24-30 I) /10

= (86)/10

= 8.6

!

8 0

3 years ago