The diameter holes for a cable harness follow a normal distr

The diameter holes for a cable harness follow a normal distribution with = 0.01 inches. For sample of size 10, an average diameter is 1.5045 inch.

(a) Find a 99% confidence interval on the mean hole diameter.

(b) Repeat this for n = 100.

Please show step by step, Thank You

Solution

a)
Confidence Interval
CI = x ± Z a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Mean(x)=1.5045
Standard deviation( sd )=0.01
Sample Size(n)=10
Confidence Interval = [ 1.5045 ± Z a/2 ( 0.01/ Sqrt ( 10) ) ]
= [ 1.5045 - 2.58 * (0.003) , 1.5045 + 2.58 * (0.003) ]
= [ 1.496,1.513 ]
b)

WHEN Sample Size(n)=100
Confidence Interval = [ 1.5045 ± Z a/2 ( 0.01/ Sqrt ( 100) ) ]
= [ 1.5045 - 2.58 * (0.001) , 1.5045 + 2.58 * (0.001) ]
= [ 1.502,1.507 ]