Answer:
Option f) None of these
Step-by-step explanation:
We are given the following data set:
Sample size, n = 12
Sample mean = 9.4
Sample standard deviation = 0.64
Confidence interval:
Putting the values, we get,

Answer:
Step-by-step explanation:
( 3+1)² * 3
= 4² * 3
= 16 * 3
= 48
Answer:
See below
Step-by-step explanation:
It has something to do with the<em> </em><u><em>Weierstrass substitution</em></u>, where we have

First, consider the double angle formula for tangent:

Therefore,

Once the double angle identity for sine is

we know
, but sure, we can derive this formula considering the double angle identity

Recall

Thus,
Similarly for cosine, consider the double angle identity
Thus,

Hence, we showed 
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Solving





Just note that

and
is not defined for 
Answer:
B) approximately normal with mean 2.3 and standard deviation 2
Step-by-step explanation:
Given the following :
Mean crimes per day = 2.3
Standard deviation = 2
Number of samples = 100
Sampling distribution of the mean:
According to the central limit theorem:
Sample mean = population mean
2.3 = 2.3
The standard deviation of the sample (s) : ratio of the population standard deviation and square root of the sample size.
s = population standard deviation / √sample size
s = 2 / √100
s = 2 / 10
s = 0.2
The central limit theorem also posits that once ths sample size is large enough, the sampling of the sample mean will be approximately normal.
Hence, the distribution is approximately normal, with mean of 2.3 and standard deviation of 0.2