Consider a sample with a mean of 50 and a standard deviation of 4. Use Chebyshev's theorem to determine the percentage of the data within each of the following ranges (to the nearest whole number).

a. 30 to 70, at least %
b. 35 to 65, at least %
c. 41 to 59, at least %
d. 38 to 62, at least %
e. 33 to 67, at least %

a)

b)

c)

d)

e)

Step-by-step explanation:

Data given  

reprsent the population mean

represent the population standard deviation

The Chebyshev's Theorem states that for any dataset

•We have at least 75% of all the data within two deviations from the mean.

•We have at least 88.9% of all the data within three deviations from the mean.

•We have at least 93.8% of all the data within four deviations from the mean.

Or in general words "For any set of data (either population or sample) and for any constant k greater than 1, the proportion of the data that must lie within k standard deviations on either side of the mean is at least:

Part a

For this case we can find the deviations from the mean like this:

Part b

For this case we can find the deviations from the mean like this:

Part c

For this case we can find the deviations from the mean like this:

Part d

For this case we can find the deviations from the mean like this:

Part e

For this case we can find the deviations from the mean like this:

c. 65°

step-by-step explanation:

we are given a triangle with two known angles, 62° and 53°, while the third angle x is unknown and we are to find its value.

we know that the sum of angles in a triangle is equal to a total of 180 degrees. so we can write it as:

x + 62° + 53° = 180°

solving to find the value of x:

x = 180 - (62 + 53) = 65°

therefore, the value of x in this triangle is 65°.

so far i think you have the right thing going for you just remember soh cah toh

step-by-step explanation:

sine over hypotenuse

cosine   equals adjacent

tangent over hypotenuse