1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
lesya692 [45]
2 years ago
14

Let X be the mean of a random sample of size n = 64 from the uniform distribution on the interval (0, 3), i.e. f(x) = ( 1 3 , 0

< x < 3 0, otherwise.
1. Approximate the probability P(1.2 < X < 2.1).
Mathematics
1 answer:
allochka39001 [22]2 years ago
6 0

Answer:

P ( 1.2 < X < 2.1 ) = 0.3

Step-by-step explanation:

Given:

Uniform distribution over interval (0,3) can be modeled by a probability density function f(x)

f(x) = 1 / (b - a)

Where a < x < b is the domain at which function is defined:

f(x) = 1 / (3) = 1 / 3

Where, X - U ( u , δ )

u = ( a + b ) / 2 = (0 +3) / 2 = 1.5

δ = ( b - a ) / sqrt (12) = (3 - 0) / sqrt (12) = 0.866

Hence,

X - U ( 1.5 , 0.866 )

There-fore calculating P ( 1.2 < X < 2.1 ):

P ( 1.2 < X < 2.1 ) = \int\limits^b_a{f(x)} \, dx

Where, a = 1.2 and b = 2.1

P ( 1.2 < X < 2.1 ) = x / 3 |

P ( 1.2 < X < 2.1 ) = 2.1 /3 - 1.2 / 3 = 0.3

Answer: P ( 1.2 < X < 2.1 ) = 0.3

You might be interested in
What can you tell about the mean of each distribution?
Mars2501 [29]

Answer:

I'm sorry I don't know ‍♀️

4 0
3 years ago
Read 2 more answers
Winnie poured 14 cups of water into a rectangular container measuring 13 inches by 7 inches by 6 centimeters.
kow [346]
Max volume = Volume of container = 13 in x 7 in x 6 in = 546 in^3 
<span>Part B: </span>
<span>1 cup = 14.4375 in^3 </span>
<span>14 cups = 14.4375 in^3 * 7 = 202.125 in^3 </span>
<span>Part C: </span>
<span>Height of water = (202.125 in^3)/(13 in x 7 in) = 2.22 in.
(i HAD THE SAME QUESTION)</span>
6 0
2 years ago
Read 2 more answers
John bought new headphones originally listed for $ 80.99 . They are \(35\%)| off. Which equation can be used to find the amount
Katarina [22]

Answer:

$28.35

Step-by-step explanation:

The headphones are $80.99 and are 35% off. To find the amount he will save, change the 35% to a decimal by moving it two times to the left, which is 0.35. Multiply 80.99 and 0.35 to get 28.3465. Round to get $28.35.

7 0
2 years ago
Because of their connection with secant​ lines, tangents, and instantaneous​ rates, limits of the form ModifyingBelow lim With h
Gre4nikov [31]

Answer:

\dfrac{1}{2\sqrt{x}}

Step-by-step explanation:

f(x) = \sqrt{x} = x^{\frac{1}{2}}

f(x+h) = \sqrt{x+h} = (x+h)^{\frac{1}{2}}

We use binomial expansion for (x+h)^{\frac{1}{2}}

This can be rewritten as

[x(1+\dfrac{h}{x})]^{\frac{1}{2}}

x^{\frac{1}{2}}(1+\dfrac{h}{x})^{\frac{1}{2}}

From the expansion

(1+x)^n=1+nx+\dfrac{n(n-1)}{2!}+\ldots

Setting x=\dfrac{h}{x} and n=\frac{1}{2},

(1+\dfrac{h}{x})^{\frac{1}{2}}=1+(\dfrac{h}{x})(\dfrac{1}{2})+\dfrac{\frac{1}{2}(1-\frac{1}{2})}{2!}(\dfrac{h}{x})^2+\tldots

=1+\dfrac{h}{2x}-\dfrac{h^2}{8x^2}+\ldots

Multiplying by x^{\frac{1}{2}},

x^{\frac{1}{2}}(1+\dfrac{h}{x})^{\frac{1}{2}}=x^{\frac{1}{2}}+\dfrac{h}{2x^{\frac{1}{2}}}-\dfrac{h^2}{8x^{\frac{3}{2}}}+\ldots

x^{\frac{1}{2}}(1+\dfrac{h}{x})^{\frac{1}{2}}-x^{\frac{1}{2}}=\dfrac{h}{2x^{\frac{1}{2}}}-\dfrac{h^2}{8x^{\frac{3}{2}}}+\ldots

\dfrac{x^{\frac{1}{2}}(1+\dfrac{h}{x})^{\frac{1}{2}}-x^{\frac{1}{2}}}{h}=\dfrac{1}{2x^{\frac{1}{2}}}-\dfrac{h}{8x^{\frac{3}{2}}}+\ldots

The limit of this as h\to 0 is

\lim_{h\to0} \dfrac{f(x+h)-f(x)}{h}=\dfrac{1}{2x^{\frac{1}{2}}}=\dfrac{1}{2\sqrt{x}} (since all the other terms involve h and vanish to 0.)

8 0
3 years ago
Chen can jump rope 60 times a minute at that rate how many jumps can he make in 9 minutes
USPshnik [31]
540, i have to write 20 characters to explain it but 540

3 0
3 years ago
Read 2 more answers
Other questions:
  • Angela opened a new bakery she got orders fir 2 cakes the first week 4 cakes the second week and 8 cakes the third week if the p
    14·1 answer
  • 98 points! please answer this question ASAP!
    10·2 answers
  • What is the value of x?<br><br> x= ___ °
    12·1 answer
  • The volume of a rectangular prism is 240 cubic centimeters. A rectangular pyramid has the same length, width, and height as the
    14·2 answers
  • ASAP!!!
    14·1 answer
  • Which trinomial is equivalent to 3(x-2)^2 -2(x-1)?
    6·1 answer
  • Simplify.<br><br> |-10| + |5|
    10·2 answers
  • Which equation would have real zero(s) corresponding to the x-intercept(s) of the graph below?
    13·1 answer
  • Graph the inequality <br> y&gt;-4x+1
    5·1 answer
  • Given: sin(x-y) -) 2 1. = cos( 17 - (x - 1) 2. = cos(I – (x+y] ( 1 / ] 3. = cos(( 1 - x)+Y [1 V 4. = cos(1 - x)-(-1] [- 5. = cos
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!