Consider a sample with a mean of 30 and a standard deviation of 5. Use Chebyshev's theorem to determine the minimum percentage of the data within each of the following ranges. (Round your answers to the nearest integer.) (a) 20 to 40 % (b) 15 to 45 % (c) 23 to 37 % (d) 17 to 43 % (e) 13 to 47

a) We are within 2 deviations from the mean since 30 -2*5 = 20 and 30 + 2*5 = 40. So our value for k = 2 and we can find the % like this:

b) We are within 3 deviations from the mean since 30 -3*5 = 20 and 30 + 3*5 = 45. So our value for k = 3 and we can find the % like this:

c) We are within 1.4 deviations from the mean since 30 -1.4*5 = 23 and 30 + 1.4*5 = 37. So our value for k = 1.4 and we can find the % like this:

d) We are within 2.6 deviations from the mean since 30 -2.6*5 = 17 and 30 + 2.6*5 = 43. So our value for k = 2.6 and we can find the % like this:

e) We are within 3.4 deviations from the mean since 30 -3.4*5 =13 and 30 + 3.4*5 = 47. So our value for k = 3.4 and we can find the % like this:

Step-by-step explanation:

For this case we need to remember what says the Chebysev theorem, and it says that we have at least of the data liying within k deviations from the mean on the interval

We know that

Part a

For this case we want the values between 20 and 40

So we are within 2 deviations from the mean since 30 -2*5 = 20 and 30 + 2*5 = 40. So our value for k = 2 and we can find the % like this:

Part b

For this case we want the values between 15 and 45

So we are within 3 deviations from the mean since 30 -3*5 = 20 and 30 + 3*5 = 45. So our value for k = 3 and we can find the % like this:

Part c

For this case we want the values between 23 and 37

So we are within 1.4 deviations from the mean since 30 -1.4*5 = 23 and 30 + 1.4*5 = 37. So our value for k = 1.4 and we can find the % like this:

Part d

For this case we want the values between 17 and 43

So we are within 2.6 deviations from the mean since 30 -2.6*5 = 17 and 30 + 2.6*5 = 43. So our value for k = 2.6 and we can find the % like this:

Part e

For this case we want the values between 13 and 47

So we are within 3.4 deviations from the mean since 30 -3.4*5 =13 and 30 + 3.4*5 = 47. So our value for k = 3.4 and we can find the % like this:

answer is 144

step-by-step explanation:

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.