Answer:
21.759
Step-by-step explanation:
Given that :
Mean (m) = 25
Standard deviation (s) = 12.5
Sample size (n) = 40
α = 90%
The confidence interval is obtained using the relation:
Mean ± Zcritical * s/sqrt(n)
Zcritical at 90% confidence interval = 1.64
25 ± 1.64 * (12.5/sqrt(40))
Lower boundary : 25 - 1.64(1.9764235) = 21.75866546
Upper boundary : 25 + 1.64(1.9764235) = 28.24133454
(21.759, 28.241)
Hence, lower bound of confidence interval is : 21.759
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Answer:
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Both of these conditions must be true in order for the assumption that the binomial distribution is approximately normal. In other words, if
and
then we can use a normal distribution to get a good estimate of the binomial distribution. If either np or nq is smaller than 5, then a normal distribution wouldn't be a good model to use.
side note: q = 1-p is the complement of probability p
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➷ 2) The integral of a constant follows this rule:
adx = ax
In this case, it is 1dx = 1x
This can be simplified to just x
Add a constant to this, to get the final answer of:
x + C
3) The integrals power rule is:

Substitute the values in:

This can be simplified to:

Add a constant to this to get the final answer of:

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