At the end of the first school day, Mr. Davies, a first grade teacher, inspected his classroom crayons. 2 of the 200 crayons w
2 answers:
Answer:
Percent of the crayons were not broken = 99 %
Step-by-step explanation:
At the end of the first school day, Mr. Davies, a first grade teacher, inspected his classroom crayons. 2 of the 200 crayons were broken.
Total number of crayons = 200
Number of crayons broken = 2
Number of crayons not broken = 200 - 2 = 198
We need to find what percent of the crayons were not broken
Percent of the crayons were not broken = 99 %
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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
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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)