Set x consists of 100 numbers. the average (arithmetic mean) of set x is 10, and the standard deviation is 4.6. which of the following two numbers, when added to set x, will decrease the set’s standard deviation by the greatest amount?
a. -100 and -100
b. -10 and -10
c. 0 and 0
d. 0 and 20
e. 10 and 10

E. 10 and 10

Step-by-step explanation:

Standard Deviation is the square root of sum of square of the distance of observation from the mean.

where, is mean of the distribution.

Here, since standard deviation is the ratio of the distance from the mean and sample size. So for decreasing the standard deviation we should keep numerator constant and increasing the denominator.

This can be only possible in option (E).

Hence, only Option (E) is correct.

17

step-by-step explanation:

51/3=17

thus 17 is your answer.

1. sometimes

2.   never

3   .08c = 7.50+.05c   250 pages

step-by-step explanation:

1.   sometimes

the theoretical probability of rolling a 1 is 1/6.   perhaps you got really lucky and never rolled a 1   in those 60 times.   your experimental probability is 0.   or perhaps you rolled a 1   20 times.   your experimental probability is 20/60 is 1/3.     it really just depends on how you rolled in that experiment.

2.   never

the probability of the event occurring is 1.   that is being 100 % sure it will happen.   that is the maximum amount of confidence we have.

3.   no customer card cost:   .08 times number of pages

customer card cost:   7.50 + .05 times number of pages

we want to find when it costs the same amount, so we will set these equal

let c = number of pages

.08c = 7.50+.05c

subtract .05c from each side

.08c-.05c = 7.5+.05c-.05c

.03c=7.5

divide each side by .03

.03c/.03 = 7.5/03

c =250  

the cost is the same at 250 pages