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
dezoksy [38]
2 years ago
14

For a normal distribution with mean equal to 31.5 and standard deviation equal to 11, what is the area under the curve that is b

etween 35 and 45?
Mathematics
1 answer:
tresset_1 [31]2 years ago
4 0

Answer:

The area is given by the following integral: \int\limits^{45}_{35} \frac{1}{\sqrt{242\pi}}e^{-\frac{(x-31.5)^2}{242}} dx, which can be approximated by: 0.265313

Step-by-step explanation:

A normal distribution is defined as:

f(x)=\frac{1}{\sqrt{2\pi \sigma^2}}e^{-\frac{(x-\mu)^2}{2\sigma^2}}

, where the greek letter sigma stands for the standard deviation and mu for the mean. Since in our problem we have a mean = 31.5 and a standard deviation = 11, then we can write this function as:

f(x)=\frac{1}{\sqrt{242\pi}}e^{-\frac{(x-31.5)^2}{242}}

Now, we need to find the area below this function, between 35 and 45, and in order to do this, we need to integrate the function. The normal distribution does not has an exact closed form integral, therefore we will have to solve the integral in a software that allows for numerical calculations (I used the online software Wolfram|Alpha).

\int\limits^{45}_{35} \frac{1}{\sqrt{242\pi}}e^{-\frac{(x-31.5)^2}{242}} dx =0.265313

You might be interested in
HELP ASAP.....NO LINKS AND NO TROLLING
Vadim26 [7]

Answer:

B. The graph of g(x) is narrower than the graph of f(x)

D.The graph g(x) is 8 units above the graph of f(x)

check the image given below.

  • The blue line refers to graph g(x)
  • The red line refers to graph f(x)

6 0
2 years ago
Read 2 more answers
Between what pair of numbers is the product of 289 and 7
LiRa [457]

The product of  289  and  7  is somewhere between  289  and 2,100 .

6 0
3 years ago
Determine if this<br> graph is an example<br> of a function.<br><br> A. Relation<br> B. Function
Mars2501 [29]

Think about what relation and function are.

Relation: can have many outputs and one input

Function: One output or one input

5 0
2 years ago
Will someone please solve this. Give answer in form of square root.
aleksklad [387]
The answer is : 46.4758001545 ( in square root )
3 0
3 years ago
Is paid an annual salary of $26,000. Find the Pat's weekly salary
elena-s [515]

Answer:500

Step-by-step explanation:26,000/52=500 i did<em> $26,000</em> divided by 52 because there are<em> </em><em>52 weeks in a year</em> and it gave me <em>500</em> so that is how i got the answer

8 0
3 years ago
Read 2 more answers
Other questions:
  • What is 5373-67567.0-790-111
    8·1 answer
  • If k, m, and t are positive integers and k + m = t , do t and 12 have a common factor 6 4 12 greater than 1 ?
    6·1 answer
  • The graph of a system of equations with the same slope will have no solutions
    5·2 answers
  • What is the theoretical probability that Marco will choose a card with a heart on it?
    12·1 answer
  • There are 20 alligators in the swamp. Each year, the number of alligators increases by 25%. There are 25 crocodiles in the swamp
    11·1 answer
  • Select all the irrational numbers
    12·1 answer
  • Geometry Chapter 4 Practice Test
    12·1 answer
  • What are two factors of 24 that add to be 10? separate each factor by a comma
    9·1 answer
  • can we just all agree that teruhashi makes watching saiki worse like every time she comes up on my tv bragging how she’s the per
    15·1 answer
  • Ten full crates of walnuts weigh 370 pounds, whereas an empty crate weighs 10 pounds. How much do the walnuts alone weigh?
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!