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
Serjik [45]
3 years ago
8

Suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.5

42.54 and a standard deviation of 0.450.45. Using the empirical rule, what percentage of the students have grade point averages that are greater than 3.443.44
Mathematics
1 answer:
masya89 [10]3 years ago
5 0

Answer:

z= \frac{3.44-2.54}{0.45}=2

P(X>3.44) = P(Z>2) = 0.025

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the grade points avergae of a population, and for this case we know the following properties

Where \mu=2.54 and \sigma=0.45

The empirical rule, also referred to as the three-sigma rule or 68-95-99.7 rule, is a statistical rule which states that for a normal distribution, almost all data falls within three standard deviations (denoted by σ) of the mean (denoted by µ). Broken down, the empirical rule shows that 68% falls within the first standard deviation (µ ± σ), 95% within the first two standard deviations (µ ± 2σ), and 99.7% within the first three standard deviations (µ ± 3σ).

So we can find the z score for the value of X=3.44 in order to see how many deviations above or belowe we are from the mean like this:

z= \frac{3.44-2.54}{0.45}=2

So the value of 3.44 is 2 deviations above from the mean, so then we know that the percentage between two deviations from the mean is 95% and on each tail we need to have (100-95)/2 = 2.5% , because the distribution is symmetrical, so based on this we can conclude that:

P(X>3.44) = P(Z>2) = 0.025

You might be interested in
What is greater 7/10 or 3/6? please show work
vovikov84 [41]
What you need to do is make sure the denominators are the same so multiply 7/10 by 6. It should now be 42/60. Next multiply 3/6 by 10. It should now equal 30/60. 7/10 = 42/60. 3/6 = 30/60. 7/10 is greater. I hope this was somewhat helpful :3
3 0
3 years ago
Read 2 more answers
Which describes a non-uniform probability model? A) heads or tails from a coin flip B) the sum result of rolling two dice C) sel
irga5000 [103]

Answer:

Option B.

Step-by-step explanation:

The non-uniform probability is when the event is not same in the occurring of event.

Option A is uniform because there will be equal chance of getting   head or tail.

Option B is non-uniform because sum can be any number  if we get(3,4) it will be 7 and if we have (2,3) then it will be 5.

Option C is uniform because we have equal number of red and green balls so, selecting a ball from both will be same.

Option D is uniform because chance of 1,2,,3,4,5 or 6 will be equal chance from rolling a die that is 1/6 in all cases.

Therefore, Option B is correct

7 0
3 years ago
Read 2 more answers
A recipe for 10 servings of raspberry sorbet calls for 2 cups of water, 1/1.2 cups of granulated sugar, and 4 cups of frozen ras
babunello [35]
We know that 16 cups are in 1 gallon
We also know that 10 servings = 2 cups


Now that means 80 servings = 1 gallon
That means we need 320 / 80=4

It is A 4 gallons 
Hope this helps
3 0
3 years ago
Read 2 more answers
LAST ATTEMPT IM MARKING AS BRAINLIEST!! (Finding missing sides- similar triangles Algebraic practice )
Dimas [21]
143 / 6x+12 = 132 / 72
143 / 6x+12 = 11 / 6

crossmultiply:
66x + 132 = 858
66x = 726
x = 11
8 0
2 years ago
Read 2 more answers
jada is using a computer’s random number generator to produce 6 random whole numbers between 1 and 100 so she can use a random s
nikdorinn [45]

Step-by-step explanation:

The random numbers are selected randomly. Just because they happen to be 6 numbers in a row does not mean that they were not. If she is confident in the random number generator, which can be assumed, then the random numbers were still randomly selected and can be used. To regenerate would be a mistake because Jada is then picking and choosing which random numbers are chosen, defeating the purpose of a random number generator

7 0
3 years ago
Other questions:
  • Find the y-intercept of 2x - 7y =28
    7·2 answers
  • WILL GIVE BRAINLIEST
    13·2 answers
  • A semicircle has an area of 76.97 km² . Find its radius
    6·2 answers
  • Si vendo los 7/4 de lo que no vendí, ¿que parte del total no vendí?
    8·1 answer
  • Sam added two fractions together and got 7/8 as the answer. Write down two fractions that Sam could of added.
    10·1 answer
  • 170°
    7·2 answers
  • Enda has job offers at two companies. One company offers a starting salary of $75,000 with a raise of $2,500 each year. The othe
    5·1 answer
  • 6. Consider the diagram below.
    7·2 answers
  • If 2x/2y=16,what is the value of x-y?
    14·1 answer
  • A shipping company charges a $6.50 flat fee for a package, plus a fee based on the weight of the package. The
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!