(50m + 5m+20m) + 10m

Let X represent the time it takes from when someone enters the line for a roller coaster until they exit on the other side. Cons

Yuri [45]

Answer:

a. E(x) = 3.730

b. c = 3.8475

c. 0.4308

Step-by-step explanation:

a.

Given

0 x < 3

F(x) = (x-3)/1.13, 3 < x < 4.13

1 x > 4.13

Calculating E(x)

First, we'll calculate the pdf, f(x).

f(x) is the derivative of F(x)

So, if F(x) = (x-3)/1.13

f(x) = F'(x) = 1/1.13, 3 < x < 4.13

E(x) is the integral of xf(x)

xf(x) = x * 1/1.3 = x/1.3

Integrating x/1.3

E(x) = x²/(2*1.13)

E(x) = x²/2.26 , 3 < x < 4.13

E(x) = (4.13²-3²)/2.16

E(x) = 3.730046296296296

E(x) = 3.730 (approximated)

b.

What is the value c such that P(X < c) = 0.75

First, we'll solve F(c)

F(c) = P(x<c)

F(c) = (c-3)/1.13= 0.75

c - 3 = 1.13 * 0.75

c - 3 = 0.8475

c = 3 + 0.8475

c = 3.8475

c.

What is the probability that X falls within 0.28 minutes of its mean?

Here we'll solve for

P(3.73 - 0.28 < X < 3.73 + 0.28)

= F(3.73 + 0.28) - F(3.73 + 0.28)

= 2*0.28/1.3 = 0.430769

= 0.4308 -- Approximated

5 0

3 years ago

When circuit boards used in the manufacture of compact disc players are tested, the long-run percentage of defectives is 5%. Let

HACTEHA [7]

Answer:

(a) The value of P (X ≤ 2) is 0.8729.

(b) The value of P (X ≥ 5) is 0.0072.

(c) The value of P (1 ≤ X ≤ 4) is 0.7154.

(d) The probability that none of the 25 boards is defective is 0.2774.

(e) The expected value and standard deviation of X are 1.25 and 1.09 respectively.

Step-by-step explanation:

The random variable X is defined as the number of defective boards.

The probability that a circuit board is defective is, p = 0.05.

The sample of boards selected is of size, n = 25.

The random variable X follows a Binomial distribution with parameters n and p.

The probability mass function of X is:

$P(X=x)={25\choose x}0.05^{x}(1-0.05)^{25-x};\ x=0,1,2,3...$

(a)

Compute the value of P (X ≤ 2) as follows:

P (X ≤ 2) = P (X = 0) + P (X = 1) + P (X = 2)

$P(X\leq =x)=\sum\limits^{2}_{x=0}{{25\choose x}0.05^{x}(1-0.05)^{25-x}}\\=0.2774+0.3650+0.2305\\=0.8729$

Thus, the value of P (X ≤ 2) is 0.8729.

(b)

Compute the value of P (X ≥ 5) as follows:

P (X ≥ 5) = 1 - P (X < 5)

$=1-\sum\limits^{4}_{x=0}{{25\choose x}0.05^{x}(1-0.05)^{25-x}}\\=1-0.9928\\=0.0072$

Thus, the value of P (X ≥ 5) is 0.0072.

(c)

Compute the value of P (1 ≤ X ≤ 4) as follows:

P (1 ≤ X ≤ 4) = P (X = 1) + P (X = 2) + P (X = 3) + P (X = 4)

$=\sum\limits^{4}_{x=1}{{25\choose x}0.05^{x}(1-0.05)^{25-x}}\\=0.3650+0.2305+0.0930+0.0269\\=0.7154$

Thus, the value of P (1 ≤ X ≤ 4) is 0.7154.

(d)

Compute the value of P (X = 0) as follows:

$P(X=0)={25\choose 0}0.05^{0}(1-0.05)^{25-0}=1\times 1\times 0.277389=0.2774$

Thus, the probability that none of the 25 boards is defective is 0.2774.

(e)

Compute the expected value of X as follows:

$E(X)=np=25\times 0.05=1.25$

Compute the standard deviation of X as follows:

$SD(X)=\sqrt{np(1-p)}=\sqrt{25\times 0.05\times (1-0.05)}=1.09$

Thus, the expected value and standard deviation of X are 1.25 and 1.09 respectively.

8 0

4 years ago

2 3/4 qt = how many pt

timofeeve [1]

2pt=1qt
1pt=1/2qt
therefor
multiply 2 and 3/4 by 1/2
(2 and 3/4) times 1/2=(2+3/4) times 1/2=2 times 1/2+3/4 times 1/2=2/2+3/8=1+3/8=1 and 3/8 pt

4 0

4 years ago

Heather earns $16

Alborosie

Answer:

$128 a day

Step-by-step explanation:

if she works 8 hours a day/ aka full time then its different from what she earns half time/4 hours, most likely she's working fulltime so ure answer would be $128 a day

(I would be happy if u marked me brainiest) thank you

8 0

3 years ago

X/6+1=3 what is x please help

belka [17]

Answer:

X = 12

Step-by-step explanation:

First you subtract 1. That gives you:

x/6 = 2.

Then you multiply by 6 to cancel out the denominator under the x. That gives you:

x = 12.

That is the value of X.

6 0

3 years ago

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(50m + 5m+20m) + 10m​

(50m + 5m+20m) + 10m