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kodGreya [7K]
3 years ago
9

A random variable is normally distributed with a mean of 25 and a standard deviation of 5. if an observation is randomly selecte

d from the distribution, determine two values of which the smallest has 25% of the values below it and the largest has 25% of the values above it.
Mathematics
1 answer:
Naddika [18.5K]3 years ago
7 0
<span>A random variable is normally distributed with a mean of 25 and a standard deviation of 5. if an observation is randomly selected from the distribution, determine two values of which the smallest has 25% of the values below it and the largest has 25% of the values above it.</span>
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Let Y be a random variable with a density function given by
Neporo4naja [7]

From the given density function we find the distribution function,

F_Y(y)=P(Y\le y)=\displaystyle\int_{-\infty}^y f_Y(t)\,\mathrm dt=\begin{cases}0&\text{for }y

(a)

F_{U_1}(u_1)=P(U_1\le u_1)=P(3Y\le u_1)=P\left(Y\le\dfrac{u_1}3\right)=F_Y\left(\dfrac{u_1}3\right)

\implies F_{U_1}(u_1)=\begin{cases}0&\text{for }u_1

\implies f_{U_1}(u_1)=\begin{cases}\frac{{u_1}^2}{18}&\text{for }-3\le u_1\le3\\0&\text{otherwise}\end{cases}

(b)

F_{U_2}(u_2)=P(3-Y\le u_2)=P(Y\ge3-u_2)=1-P(Y

\implies F_{U_2}(u_2)=\begin{cases}0&\text{for }u_2

\implies f_{U_2}(u_2)=\begin{cases}\frac32(u_2-3)^2&\text{for }2\le u_2\le4\\0&\text{otherwise}\end{cases}

(c)

F_{U_3}(u_3)=P(Y^2\le u_3)=P(-\sqrt{u_3}\le Y\le\sqrt{u_3})=F_Y(\sqrt{u_3})-F_y(\sqrt{u_3})

\implies F_{U_3}(u_3)=\begin{cases}0&\text{for }u_3

\implies f_{U_3}(u_3}=\begin{cases}\frac32\sqrt u&\text{for }0\le u\le1\\0&\text{otherwise}\end{cases}

5 0
3 years ago
Find the volume please
Mashutka [201]

Answer:

Volume = 4/3 πr³

V = 4/3*22.7*8

V = 32.656 m³

8 0
2 years ago
Pls!!!!!!!!!!!!!!!!!!!!​
lesya692 [45]

Answer:

C

Step-by-step explanation:

The table shows a linear function.

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = \frac{y_{2}-y_{1}  }{x_{2}-x_{1}  }

with (x₁, y₁ ) = (1, 3) and (x₂, y₂ ) = (2, 7) ← 2 ordered pairs from the table

m = \frac{7-3}{2-1} = 4, thus

y = 4x + c ← is the partial equation

To find c substitute any ordered pair into the partial equation

Using (1, 3), then

3 = 4 + c ⇒ c = 3 - 4 = - 1

y = 4x - 1 → C

3 0
3 years ago
Which expression is equivalent to 3√32x^8y^10?
denpristay [2]
<span>
3√(32x^8y^10)
= </span><span>3√(16*2 x^8y^10)
= 12x^4y^5 </span>√2

Hope it helps
6 0
3 years ago
Read 2 more answers
If a coin has been altered so that the probability of heads coming up is 3/10, then the probability of tails coming up is also 3
soldier1979 [14.2K]
False. In a coin, there are 2 possible out comes i.e. a head and a tail. if p is the probability of one side coming up, then the probability of the other side comin up will be q = 1 - p.

Therefore, if the probability of head coming up is 3/10, the probability of tail coming up will be 1 - 3/10 = 7/10.
8 0
3 years ago
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