Need a better explaintion with full details on how to solve part (a) and (b) Ind

Question

Need a better explaintion with full details on how to solve part (a) and (b)

Industry specification on the diameter of a typical hole drilled in a miniature metal part using electrical discharge machining is 0.310 in. A group of students collected data to verify if these specifications are met. The diameters were measured on a sample of size 50, which produced a mean of 0.346 in, and a sample standard deviation s = 0.078 in. Assume that the holes the students measured were representative of the output of a physically stable drilling process. a. Give a 95% two-sided confidence interval for the mean diameter of holes drilled by this process. Round to the nearest thousandth. b. Give a 95% upper confidence bound for the mean diameter of holes drilled by this process. Round to the nearest thousandth.

Explanation / Answer

here sample mean=0.346, sample standard deviation s=0.078, sample size=50

since sample size is more than 30 so we can use z-value for calculating confidence interval

(a) (1-alpha)*100% confidence interval for population mean=sample mean± z(alpha/2)*s/sqrt(n)

95% confidence interval for population mean=sample mean±z(0.05/2)*s/sqrt(n)=0.346±1.96*0.078/sqrt(50)

=0.346±0.022=(0.324, 0.368)

(b) 95% upper confidence bound=0.368

since the 95% confidence interval for population mean=(0.324, 0.368)

so 95% lower confidence bound=0.324 and

95% upper confidence bound=0.368 and

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