1+4=5 2+5=12. 3+6=21. 8+11=?
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For the given standard deviation and sample mean the two sided confidence interval on mean diameter foe 95% and 99% is given by ( 1.4983 , 1.5107 ) and ( 1.49635 , 1.51265 ) respectively.
As given in the question,
Confidence interval for population mean is given by:
± z × ( σ / √n)
Where,
σ = population standard deviation.
n= sample size
= Sample mean
Given values from the random sample size are :
σ = 0.01 inches
n= 10
= 1.5045
Critical value confidence interval (using x-value table)
z for 99% = 2.576 and Significance level = 0.01
z for 95% = 1.960 and Significance level = 0.05
99% two-sided confidence interval on the mean hole diameter is equal to :
± z × ( σ / √n)
= 1.5045 ± 2.576 × ( 0.01 / √10)
= 1.5045 ± 0.00815 (approximately)
= 1.5045 - 0.00815 , 1.5045 + 0.00815
= ( 1.49635 , 1.51265 )
95% two-sided confidence interval on the mean hole diameter is equal to :
± z × ( σ / √n)
= 1.5045 ± 1.960 × ( 0.01 / √10)
= 1.5045 ± 0.00620 (approximately)
= 1.5045 - 0.00620 , 1.5045 + 0.00620
= ( 1.4983 , 1.5107 )
Therefore, for the given standard deviation and sample mean the two sided confidence interval on mean diameter foe 95% and 99% is given by ( 1.4983 , 1.5107 ) and ( 1.49635 , 1.51265 ) respectively.
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Assuming you mean f(t) = g(t) × h(t), notice that
f(t) = g(t) × h(t) = cos(t) sin(t) = 1/2 sin(2t)
Then the difference quotient of f is
Recall the angle sum identity for sine:
sin(x + y) = sin(x) cos(y) + cos(x) sin(y)
Then we can write the difference quotient as
or
(As a bonus, notice that as h approaches 0, we have (cos(2h) - 1)/(2h) → 0 and sin(2h)/(2h) → 1, so we recover the derivative of f(t) as cos(2t).)