Complete the table. (Round your answers to five decimal places. Assume x is in terms of radian.) 3 sin
lim
X --
X
х
-0.1
-0.01
-0.001
0
0.001
0.01
0.1
f(x)
2.99500
0.05235
x
0.05235
X
?
0.05235
X
0.05235
x
2.99500
✓
lim
Use the result to estimate the limit. Use a graphing utility to graph the function to confirm your result. (Round your answer to five decimal places.)
3 sin x
- 3
x-0
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i think the answer is d im not sure

irst, find the z score of a score of 80. this is given by the formula z = (x-u)/o, where x is the score, u is the mean, and o is the standard deviation. this gives

z = (80-78)/12 = 1/6 = .1667

now, find what percentile a z score of 1/6 correlates to in the normal distribution.

a z score of 1/6 = .1667 is equivalent to the 56.36th percentile of the distribution. so the probability a score is over this is 1-.5636 = .4364

the mean of a sample mean is equal to the original mean. however, the standard deviation of a sample mean is equal to the original standard deviation divided by the square root of n (sample size). so the new standard deviation is 12/sqrt(16) = 3.

the new z score is 80-78/3 = 2/3 = .667. this is equivalent to the 74.86th percentile. so the probability that the mean will be greater than this score is 1-.7486 = .2514.