Mathematics, 25.05.2020 18:58 caitlyn73

A data set with a mean of 34 and a standard deviation of 2.5 is normally distributed.
According to the Empirical Rule, what percent of the data is in each of the following ranges? Round to the nearest tenth of a percent if necessary.

Between
34 and 39 Less than 31.5 Between
29 and 36.5
Percentage
%
%
%

Answers: 1

Show answers

Answers

Answer from: Rusven

a) From the mean and 2 deviations above we have 95/2% = 47.5% of the data

b) Below one deviation from the mean we have (50-34)% =16% of the data

c) One deviation below the mean and 2 deviations above we have (47.5%) +34% = 81.5% of the data

Step-by-step explanation:

For this case we know that for a random variable X we have:

$X \sim N(\mu = 34, \sigma =2.5)$

The empirical rule states that within one deviation from the mean we have 68% of the values, within 2 deviations 95% and ithin 3 deviations 99.7% of the data.

So then we want to find the % between 34 and 39. We can use the z score formula given by:

$z =\frac{X-\mu}{\sigma}$

In order to calculate the deviations from the mean and replacing we got:

$z = \frac{34-34}{2.5}=0$

$z = \frac{39-34}{2.5}=2$

And from the mean and 2 deviations above we have 95/2% = 47.5% of the data

For the probability that would be less than 31.5 we find the z score:

$z = \frac{31.5-34}{2.5}=-1$

And below one deviation from the mean we have (50-34)% =16% of the data

And for the last part between 29 and 36.5 we find the z scores and we got:

$z = \frac{29-34}{2.5}=-2$

$z = \frac{36.5-34}{2.5}=1$

And from one deviation below the mean and 2 deviations above we have (47.5%) +34% = 81.5% of the data

Answer from: Quest

5=812a+9+3

step 1: simplify both sides of the equation.

5=812a+9+3

5=(812a)+(9+3)(combine like terms)

5=812a+12

step 2: flip the equation.

812a+12=5

step 3: subtract 12 from both sides.

812a+12−12=5−12

812a=−7

step 4: divide both sides by 812.

812a /812 = -7/812

a= -1/116

so the answer is

a= -1/116

Answer from: Quest

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

$\tan\left(x\right)=\frac{\left[altitude\right]}{\left[base\right]}=\frac{p}{r}$