Evaluate and answer in standard form: 3^-1

What is two thirds or 2/3 of the whole 120

Zepler [3.9K]

It would be 80 because 2 times 120 is 240. 240 divided by 3 is 80

3 0

2 years ago

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

masya89 [10]

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:

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

5 0

2 years ago

A box of oranges weighs 4kg. if one orange weighs 80 g how many oranges are in the box?

wlad13 [49]

Answer:

50 Oranges is your answer.

Step-by-step explanation:

Lets see..

4 kg = 4000 grams mainly because 1kg = 1000 grams in total.

4000 grams divided by 80 grams will give you the number of oranges that the box has since each orange weighs 80 grams.

4000/80 = 50.

hope this helps!

5 0

2 years ago

Read 2 more answers

Prove that the triangle EDF is isosceles. Give reasons for your answer.

Gekata [30.6K]

Answer:

$\triangle EDF$ is isosceles.

Step-by-step explanation:

Please have a look at the attached figure.

We are given the following things:

$\angle EDF = y$

$\text{External }\angle DFG = 90 +\dfrac{y}{2}$

Let us try to find out $\angle E$ and $\angle DFE$ . After that we will compare them.

Finding  $\angle DFE$ :

Side EG is a straight line so $\angle GFE = 180$

$\angle GFE$ is sum of internal $\angle DFE$ and external $\angle DFG$

$\angle GFE = 180 = \angle DFE + \angle DFG\\\Rightarrow 180 = \angle DFE + (90+\dfrac{y}{2})\\\Rightarrow \angle DFE = 180 - 90 - \dfrac{y}{2}\\\Rightarrow \angle DFE = 90 - \dfrac{y}{2} ....... (1)$