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
dangina [55]
3 years ago
14

Test scores of the student in a school are normally distributed mean 85 standard deviation 3 points. What's the probability that

a random selected student score is greater than 76

Mathematics
1 answer:
Mrrafil [7]3 years ago
5 0

Answer:

The probability that a random selected student score is greater than 76 is \\ P(x>76) = 0.99865.

Step-by-step explanation:

The Normally distributed data are described by the normal distribution. This distribution is determined by two <em>parameters</em>, the <em>population mean</em> \\ \mu and the <em>population standard deviation</em> \\ \sigma.

To determine probabilities for the normal distribution, we can use <em>the standard normal distribution</em>, whose parameters' values are \\ \mu = 0 and \\ \sigma = 1. However, we need to "transform" the raw score, in this case <em>x</em> = 76, to a z-score. To achieve this we use the next formula:

\\ z = \frac{x - \mu}{\sigma} [1]

And for the latter, we have all the required information to obtain <em>z</em>. With this, we obtain a value that represent the distance from the population mean in standard deviations units.

<h3>The probability that a randomly selected student score is greater than 76</h3>

To obtain this probability, we can proceed as follows:

First: obtain the z-score for the raw score x = 76.

We know that:

\\ \mu = 85

\\ \sigma = 3

\\ x = 76

From equation [1], we have:

\\ z = \frac{76 - 85}{3}

Then

\\ z = \frac{-9}{3}

\\ z = -3

Second: Interpretation of the previous result.

In this case, the value is <em>three</em> (3) <em>standard deviations</em> <em>below</em> the population mean. In other words, the standard value for x = 76 is z = -3. So, we need to find P(x>76) or P(x>-3).

With this value of \\ z = -3, we can obtain this probability consulting <em>the cumulative standard normal distribution, </em>available in any Statistics book or on the internet.

Third: Determination of the probability P(x>76) or P(x>-3).

Most of the time, the values for the <em>cumulative standard normal distribution</em> are for positive values of z. Fortunately, since the normal distributions are <em>symmetrical</em>, we can find the probability of a negative z having into account that (for this case):

\\ P(z>-3) = 1 - P(z>3) = P(z

Then

Consulting a <em>cumulative standard normal table</em>, we have that the cumulative probability for a value below than three (3) standard deviations is:

\\ P(z

Thus, "the probability that a random selected student score is greater than 76" for this case (that is, \\ \mu = 85 and \\ \sigma = 3) is \\ P(x>76) = P(z>-3) = P(z.

As a conclusion, more than 99.865% of the values of this distribution are above (greater than) x = 76.

<em>We can see below a graph showing this probability.</em>

As a complement note, we can also say that:

\\ P(z3)

\\ P(z3)

Which is the case for the probability below z = -3 [P(z<-3)], a very low probability (and a very small area at the left of the distribution).

You might be interested in
Naviah buys 8 but no more than 12 gallons of gas each week. The price of gas ranged from $2.25 to $2.50 each week. Write a compo
aleksklad [387]

Answer:

b

Step-by-step explanation:

8 0
2 years ago
3x-4y=28 find slope intercept form
Helen [10]
First you have to subtract 3x and then divide everything by -4 to get y=3/4x-7
6 0
3 years ago
Given two vectors a⃗ = 4.60 i^+ 7.20 j^ and b⃗ = 5.10 i^− 2.70 j^ , find the scalar product of the two vectors a⃗ and b⃗ .
grin007 [14]
A=<4.60,7.20>
b=<5.10,2.70>
The scalar product, or the inner product, or the dot-product, is by summing the products of the respective directions, 
a.b=4.6*5.1+7.2*2.7
=23.46+19.44
=42.9
6 0
3 years ago
RADIO TELESCOPES The cross section of a large radio telescope is a parabola. The equation that describes the cross section is y=
Minchanka [31]

Answer:

I am sorry

Step-by-step explanation:

3 0
3 years ago
Keisha has $20.08 in her purse. She buys a book for $8.72 . How much does she have left?
torisob [31]
Simply subtract 8.72 from 20.08 and you get the answer which is 11.36$
7 0
3 years ago
Read 2 more answers
Other questions:
  • Factorise the following
    5·1 answer
  • What is the area of the area of this figure? use 3.14 for pi
    7·1 answer
  • HELPPPPPPPPPPPPPPPPPPP
    10·1 answer
  • Find an equation of the line that
    13·1 answer
  • There was a surplus of office space in a city, with 400,000 square feet, or 16% of the total office space, vacant. How much offi
    12·1 answer
  • (-1/3x+9.5)+ x(3/4+2.5)
    6·2 answers
  • Sally bought five books.Their mean price was 3.25. The total cost for four books was 11.75.what was the cost of the fifth book​
    15·1 answer
  • What are the zeros of fx) =-8x+ 16? Yes
    5·2 answers
  • Correct answer gets brainliest and 5 stars
    15·2 answers
  • Two fractions between 2 and 2 1/2
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!