Please help with this AP Calculus question!
1 answer:
9514 1404 393
Answer:
B. -1
Step-by-step explanation:
A graph can show you that the expression approaches -1 as x approaches 2π.
The limit is -1.
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The expression evaluated at x=2π is 0/0, an indeterminate form. This suggests that L'Hopital's rule is applicable. Applying that, we have ...
lim = (f'(2π) -f'(x))/(x-2π)' = -cos(x)/1
Evaluated at x=2π, this is ...
lim = -1
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Using the normal distribution, it is found that there was a 0.9579 = 95.79% probability of a month having a PCE between $575 and $790.
<h3>Normal Probability Distribution</h3>The z-score of a measure X of a normally distributed variable with mean and standard deviation
is given by:
- The z-score measures how many standard deviations the measure is above or below the mean.
- Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
The mean and the standard deviation are given, respectively, by:
.
The probability of a month having a PCE between $575 and $790 is the <u>p-value of Z when X = 790 subtracted by the p-value of Z when X = 575</u>, hence:
X = 790:
Z = 1.8
Z = 1.8 has a p-value of 0.9641.
X = 575:
Z = -2.5
Z = -2.5 has a p-value of 0.0062.
0.9641 - 0.0062 = 0.9579.
0.9579 = 95.79% probability of a month having a PCE between $575 and $790.
More can be learned about the normal distribution at brainly.com/question/4079902
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