Find the elapsed time between 4:16 p.m. and 9:25 p.m.
1 answer:
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The given statement is true.
In general, the growth rate of exponential functions is far greater than the quadratic function. This can be illustrated through an example.
Consider an exponential function
and a quadratic function 
.
Note that the leading coefficient of the quadratic function is far greater than the base of the exponential function but still the exponential function will exceeds the quadratic function after x = 15.664 as shown in the graph below.
Therefore, we can conclude that the given statement is correct.
In general, the growth rate of exponential functions is far greater than the quadratic function. This can be illustrated through an example.
Consider an exponential function
Note that the leading coefficient of the quadratic function is far greater than the base of the exponential function but still the exponential function will exceeds the quadratic function after x = 15.664 as shown in the graph below.
Therefore, we can conclude that the given statement is correct.
Using the Central Limit Theorem, we have that:
a) Yes, it can be used, as np > 10 and n(1 - p) > 10.
b) There is a 0.0475 = 4.75% probability that the proportion in the random sample of 100 orders is the same as the proportion found in the audit sample or less.
<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.
- By the Central Limit Theorem, for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean
and standard deviation
, as long as
and
.
For the sample, we have that:
- np = 85 > 10.
- n(1 - p) = 15 > 10.
Hence the normal approximation can be used.
As for part B, if we have p = 0.9 and n = 100, the mean and the standard error are given by:
.
The probability of a sample proportion of 85% of less is the <u>p-value of Z when X = 0.85</u>, hence:
By the Central Limit Theorem
Z = -1.67
Z = -1.67 has a p-value of 0.0475.
There is a 0.0475 = 4.75% probability that the proportion in the random sample of 100 orders is the same as the proportion found in the audit sample or less.
More can be learned about the Central Limit Theorem at brainly.com/question/24663213
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