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A telephone company offers a monthly cellular phone plan for $20.00. It includes 350 free minutes plus $0.25 per minute for additional minutes. The following
function gives the monthly cost for a subscriber, where x is the number of minutes used.
20.00
if OS X s 350
C(x) =
if x > 350
= { 20.00 +0.256x - 350)
Simplify the expression in the second line of the piecewise function. Then use point-plotting to graph the function
Fill in the simplified expression below.
C(x) =
{
20.00
if Os x s350
if x > 350
(Use integers or decimals for any numbers in the expression. Do
not factor)
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the answer is c

step-by-step explanation:

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.