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Suppose that X has an exponential distribution with mean equal to 10. Determine the following: a. P(X > 10) b. P(X > 20) c

GrogVix [38]

Answer:

(a) The value of P (X > 10) is 0.3679.

(b) The value of P (X > 20) is 0.1353.

(c) The value of P (X < 30) is 0.9502.

(d) The value of x is 30.

Step-by-step explanation:

The probability density function of an exponential distribution is:

$f(x)=\lambda e^{-\lambda x};\ x>0, \lambda>0$

The value of E (X) is 10.

The parameter λ is:

$\lambda=\frac{1}{E(X)}=\frac{1}{10}=0.10$

(a)

Compute the value of P (X > 10) as follows:

$P(X>10)=\int\limits^{\infty}_{10} {0.10 e^{-0.10 x}} \, dx \\=0.10\int\limits^{\infty}_{10} { e^{-0.10 x}} \, dx\\=0.10|\frac{e^{-0.10 x}}{-0.10} |^{\infty}_{10}\\=|e^{-0.10 x} |^{\infty}_{10}\\=e^{-0.10\times10}\\=0.3679$

Thus, the value of P (X > 10) is 0.3679.

(b)

Compute the value of P (X > 20) as follows:

$P(X>20)=\int\limits^{\infty}_{20} {0.10 e^{-0.10 x}} \, dx \\=0.10\int\limits^{\infty}_{20} { e^{-0.10 x}} \, dx\\=0.10|\frac{e^{-0.10 x}}{-0.10} |^{\infty}_{20}\\=|e^{-0.10 x} |^{\infty}_{20}\\=e^{-0.10\times20}\\=0.1353$

Thus, the value of P (X > 20) is 0.1353.

(c)

Compute the value of P (X < 30) as follows:

$P(X$

Thus, the value of P (X < 30) is 0.9502.

(d)

It is given that, P (X < x) = 0.95.

Compute the value of x as follows:

$P(X$

Take natural log on both sides.

$ln(e^{-0.10x})=ln(0.05)\\-0.10x=-2.996\\x=\frac{2.996}{0.10}\\ =29.96\\\approx30$

Thus, the value of x is 30.

7 0

3 years ago

I need help with this one too

natali 33 [55]

Hey there! :)

Answer:

y = 11.

Step-by-step explanation:

Set both of the equations equal:

5x - 9 = x² - 3x + 7

Rearrange the equation:

0 = x² - 3x - 5x + 9 + 7

Combine like terms:

0 = x² - 8x + 16

Factor:

0 = (x -4)²

Solve for x:

0 = x - 4

x = 4.

Plug this into an equation to solve for 'y':

y = 5(4) - 9

y = 20 - 9

y = 11.

3 0

3 years ago

Read 2 more answers

Click on the graphic to select the figure that would make the following a reflection in line k

Roman55 [17]

I remember answering the same question, but you didn't attach any photos. But I remember that the answer is the first one.

I hope I helped. Stay safe and God bless!

- Eli <3

6 0

3 years ago

If f(x)=2(x-3)+4, what is: f(-2)

Vlad1618 [11]

Answer:

f(-2) = -6

Step-by-step explanation:

2(-2-3) + 4

2(-5) + 4

-10 + 4

-6

3 0

3 years ago

. In the past decades there have been intensive antismoking campaigns sponsored by both federal and private agencies. In one stu

Sergeeva-Olga [200]

Answer: B. $H_0:p_1=p_2$

$H_a:p_1>p_2$

Step-by-step explanation:

Let $p_1$ be the proportion of all U.S. adults that smoked in 1995. Let $p_2$ denote the proportion of all U.S. adults that smoked in 2000.

Objective for the study : Whether the proportion of U.S. adults that smoke declined during the 5-year period between the samples.

i.e. $p_1>p_2$

Alternative hypothesis $(H_a)$ is the statement containing population parameter that shows there is significant difference between the groups being tested.

⇒ $H_a:p_1>p_2$

Null hypothesis $(H_0)$ is the statement containing population parameter that shows there is no significant difference between the groups being tested.

⇒ $H_0:p_1=p_2$

Hence, The hypotheses to test in this problem are

$H_0:p_1=p_2$

$H_a:p_1>p_2$

Hence, the correct answer is B. $H_0:p_1=p_2$

$H_a:p_1>p_2$

8 0

3 years ago