(CO 3) Sixty-five percent of products come off the line ready to ship to distributors. Your quality control department selects 1
2 products randomly from the line each hour. Looking at the binomial distribution, if fewer than how many are within specifications would require that the production line be shut down (unusual) and repaired?
1 answer:
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Let X be the length of rulers. X follows Normal distribution with mean μ and standard deviation σ = 0.02. A sample of size n=4 is drawn from population and sample mean m=1000. We have to find 90% confidence interval for population mean μ.
Here population standard deviation is given to us so we will use z confidence interval for mean. It is given as
(Sample mean - Margin of error , Sample mean + Margin of error)
Where margin of error for z confidence interval is
ME = σ
Where σ = population standard deviation = 0.02
n= sample size =4
= Critical z score value for given confidence level
We have to find here 90% confidence interval so confidence level c= 0.9
α = 1 -c =1-0.9 = 0.1
=
=
Here we have to find z score value such that area below it is -z is 0.05 and above z is 0.05
Using excel function to find z score value
=NORM.S.INV(0.05) = -1.645
For calculating confidence interval we consider positive z score value which is 1.645
So the margin of error is
ME =
ME = 0.01645
90% confidence interval for mean is
(Sample mean - ME, Sample mean+ME)
1000- 0.01645, 1000+0.01645
(1000.01645, 999.9836)
Rounding interval upto 3 decimal places
(1000.016, 999.984)
90% confidence interval for population mean is (1000.016, 999.984)
Answer:
Third option:
Step-by-step explanation:
<h3> The correct exercise is attached.</h3>
The equation given is:
The steps to find the value of "x" are shown below:
1. Add 2 to both sides of the equation:
2. Descompose 9 and 27 into their prime factors:
3. Substitute them into the equation:
4. Knowing that If , then
, we get:
5. Apply Distributive property:
6. Add 2 to both sides:
7. Divide both sides of the equation by 2:
