Find out the expected value and the standard deviation of the number of aces obtained in 60 rolls of a fair 6-face die. ditto for 600 rolls. use them to explain why the observed count of aces obtained is more likely to be within 2 from the expected value with 60 rolls than with 600 rolls.

Step-by-step explanation:

Lets call X the amount of aces obtained in 60 rolls, and Y the amount of aces obtained in 600 rolls.

Note that both X and Y are obtained from counting the amount of successful tries from repetitions of independent experiments that have 1/6 of probability of success. Thus, both X and Y are random variables with binomial distribution, with n = 60 and 600 respectively and probability 1/6.

Remember that if Z is a random variable, Z ≈ Bi(n,p), then

As a result

The observed amount of aces is more likely to be closer from the expected value with 60 rolls because, since we have less rolls, it is more difficult to obtain spread results.

You can also notice that X and Y can be obtained by summing independent variables with distribution BI(1,p) (also called Bernoulli(p) ). When you sum independent variables with the same distribution you have this property:

X can be obtained by summing 60 independent variables r1, , r60 with mean 1/6 and variance 1/6*(5/6) = 5/36. So we obtain that V(X) = 60*5/36, and sd(X) = √60 * √(5/36). While for the same argument sd(Y) = √600*√(5/36). The higher the number of rolls, the more spread the results are.

I hope this helped you!

answer: sorry i can't you.

step-by-step explanation:

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be