a. Calculation of critical value at 95% confidence level44

Alpha = 1005 - 95% = 5%

Alpha = 0.05

Alpha / 2 = 0.025

Area in the middle = 1-0.025 = 0.975

From z table, critical value = 1.96 (from table against 0.975)

b. Given

sample size = 144

sample mean = 8 minutes

standard deviation = 3 minutes

Therefore, population mean = sample mean (+/-) (critical value* standard deviation / Square root of sample size)

= 8 (+/-) (1.96*3/(144)^0.5))

Population mean of drill times = 8 (+/-) 0.49 minutes

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