Answer:
Step-by-step explanation:
From the information given,
Mean, μ = 4.2 mm
Standard deviation, σ = 0.1 mm
number of sample, n = 87
1) For a confidence level of 98%, the corresponding z value is 2.33.
We will apply the formula
Confidence interval
= mean ± z ×standard deviation/√n
It becomes
4.2 ± 2.33 × 0.1/√87
= 4.2 ± 2.33 × 0.0107
= 4.2 ± 0.025
b) The lower end of the confidence interval is 4.2 - 0.025 =4.18
The upper end of the confidence interval is 4.2 + 0.025 =4.23
c) 0.015 = 2.33 × 0.1/√n
0.015/2.33 = 0.1/√n
0.00644 = 0.1/√n
√n = 0.1/0.00644 = 16
n = 16² = 256
d) For a confidence level of 90%, the corresponding z value is 1.645.
It becomes
4.2 ± 1.645 × 0.1/√87
= 4.2 ± 1.645 × 0.0107
= 4.2 ± 0.0176
The upper bound for the mean thickness is
4.2 + 0.0176 = 4.2176mm
