Please help! Will Mark brainliest!

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Answer 1

Answer:

Answer:

Step-by-step explanation:

i not fully sure if this is right

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NBC News reported on May 2, 2013, that 1 in 20 children in the United States have a food allergy of some sort. Consider selecting a random sample of 15 children and let X be the number in the sample who have a food allergy. Then X ~ Bin(15, 0.05). (Round your probabilities to three decimal places.) (a) Determine both P(X ≤ 3) and P(X < 3). P(X ≤ 3) = P(X < 3) = (b) Determine P(X ≥ 4). P(X ≥ 4) = (c) Determine P(1 ≤ X ≤ 3). P(1 ≤ X ≤ 3) = (d) What are E(X) and σX? (Round your answers to two decimal places.) E(X) = σX = (e) In a sample of 90 children, what is the probability that none has a food allergy?

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Answer:

a) P(X ≤ 3) = 0.9946

P(X < 3) = 0.9639

b) P(X ≥ 4) = 0.0054

c) P(1 ≤ X ≤ 3) = 0.5313

d) E(X) = 0.75

σX = 0.84

e) P(X=0) = 0.0099

Step-by-step explanation:

We have x: number in the sample who have a food allergy. As the sample is of n=15 and p=0.05, we have:

$X \sim Bin(15, 0.05)$

a) We have to determine P(X ≤ 3) and P(X < 3)

We can calculate P(X ≤ 3) as the sum of P(0), P(1), P(2) and P(3).

$P(x\leq 3)=\sum_(k=0)^3P(k)\n\n\nP(x=0) = \binom{15}{0} p^(0)q^(15)=1*1*0.4633=0.4633\n\nP(x=1) = \binom{15}{1} p^(1)q^(14)=15*0.05*0.4877=0.3658\n\nP(x=2) = \binom{15}{2} p^(2)q^(13)=105*0.0025*0.5133=0.1348\n\nP(x=3) = \binom{15}{3} p^(3)q^(12)=455*0.0001*0.5404=0.0307\n\n\nP(x\leq 3)=0.4633+0.3658+0.1348+0.0307=0.9946$

P(x<3) can be calculated from the previos result as:

$P(x<3)=P(X\leq3)-P(3)=0.9946-0.0307=0.9639$

b) We can calculate P(X ≥ 4) as:

$P(X\geq4)=1-P(X<4)=1-P(X\leq3)=1-0.9946=0.0054$

c) We can calculate P(1 ≤ X ≤ 3) as:

$P(1 \leq X \leq 3)=P(1)+P(2)+P(3)=0.3658+0.1348+0.0307=0.5313$

d) The expected value of a binomial variable is the product of the sample size n and the probability of success p:

$E(X)=np=15*0.05=0.75$

The standard deviation is calculates as:

$\sigma_x=√(np(1-p))=√(15*0.05*0.95)=√(0.7125) =0.84$

e) In this case, the sample size is n=90.

We can calculate the probability that none has a food allergy as:

$P(x=0) = \binom{90}{0} p^(0)q^(90)=0.95^(90)=0.0099$

Calculeaza aria unui triunghi cu baza de 20 cm si inaltimea corespunzatoare ei de 12 cm

Answers

Answer:

Aria unui triunghi =120 cm²

Step-by-step explanation:

Folosind formula:

Aria unui triunghi = (baza x înălțimea) / 2

A=(20x12)/2

=240/2 cm²

=120 cm²

Aria unui triunghi =120 cm²

Which equation has the same solution as x -12 = 40

Answers

Steps to solve:

x - 12 = 40

~Ad 12 to both sides

x = 52

Best of Luck!

I need help quick A student is cutting a square out of a piece of poster board. The area of the poster board can be represented as (4x ^ 2 + 14x - 8) in ^ 2 The area of the square can be represented as (x ^ 2 + 8x + 16) in^2 Write an expression to represent the area of the poster board left over after the student cuts out the square

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Answer:

area left = (3x² + 6x - 24) in²

Step-by-step explanation:

the area of poster board left

= area of poster board - area of square cut out

= 4x² + 14x - 8 - (x² + 8x + 16) ← distribute parenthesis by - 1

= 4x² + 14x - 8 - x² - 8x - 16 ← collect like terms

= (4x² - x² ) + (14x - 8x) + (- 8 - 16)

= 3x² + 6x + (- 24)

= (3x² + 6x - 24) in²

Simplify 2^3 + 6^1 =

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Answer:

Step-by-step explanation:

2^3=8

6^1=6

8+6=14

Answer:

2^3+6^1

8+6

Step-by-step explanation:

2^3 can be expanded to 2x2x2 which equals 8

6^1 can be expanded to 6x1 which is 6

2^3+6^1 can be simplified to to 8+6

8+6 is 14

Form a polynomial f(x) with real coefficients having the given degree and zeros.Degree 4; zeros: 1, multiplicity 2; 2i

Answers

Answer:

Step-by-step explanation:no

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