Problem 3 Week 6 (1)
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Mt. Kenya University *
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Industrial Engineering
Date
Nov 24, 2024
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Uploaded by DeanSteel624
Problem #3
If the manager of a bottled water distributor wants to estimate, with 95% confidence, the mean
amount of water in a 1-gallon bottle to within
±0.002 gallons and also assumes that the standard deviation is 0.03 gallons, what sample size is
needed?
𝑛 = (𝑍2.
σ2
𝐸2
)
Z = 1.96 (corresponds to 95% confidence level)
σ =
0.03
E = 0.002
n = 1.96
2
x 0.03
2
÷ 0.002
2
n = 864.36
n = 864
If a light bulb manufacturing company wants to estimate, with 95% confidence, the mean life of
compact fluorescent light bulbs to within ±150 hours and also assumes that the population
standard deviation is 1100 hours, how many compact fluorescent light bulbs need to be selected?
𝑛 = (𝑍2.
σ2
𝐸2
)
Z = 1.96 (corresponds to 95% confidence level)
σ = 1100
E = 150
n = 1.96
2
x 1100
2
÷ 150
2
n = 206.5927
n = 207
If the inspection division of a county weights and measures department wants to estimate the
mean amount of soft drink fill in 2-liter bottles to within ±0.02 liter with 99% confidence and
also assumes that the standard deviation is 0.06 liters, what sample size is needed?
𝑛 = (𝑍2.
σ2
𝐸2
)
Z = 2.576 (corresponds to 99% confidence level)
σ = 0.06
E = 0.02
n = 2.576
2
x 0.06
2
÷ 0.02
2
n = 59.7219
n = 60
An advertising executive wants to estimate the mean amount of time that consumers spend with
digital media daily. From past studies, the standard deviation is estimated as 49 minutes. What
sample size is needed if the executive wants to be 95% confident of being correct to within ±4
minutes?
𝑛 = (𝑍2.
σ2
𝐸2
)
Z = 1.96 (corresponds to 95% confidence level)
σ = 49
E = 4
n = 1.96
2
x 49
2
÷ 4
2
n = 576.4801
n = 576
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