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1.Find the critical value zc necessary to form a confidence interval at the given level of
confidence. a.90% b.97%
a) zc = 1.645
b) zc = 2.17
2.A group of 40 bowlers showed that their average score was 192. The population
standard deviation is known to be 8. a.Find the margin of error E for a 95% confidence
interval. Round your answer to the nearest tenths. b.Construct a 95% confidence interval
for the mean score, ? of all bowlers.
a) Margin of error, E = zc*σ/√n = 1.96*8/√40 = 2.479 = 2.5
b) A 95% confidence interval for the mean score is given by
(Xbar – E, Xbar + E) = (192 – 2.5, 192 + 2.5) = (189.5, 194.5)
3. In order to fairly set flat rates for auto mechanics, a shop foreman needs to estimate the
average time it takes to replace a fuel pump in a car. How large a sample must he select if
he wants to be 99% confident that the true average time is within 15 minutes of the
sample average? Assume the standard deviation of all times is 30 minutes.
The required sample size, n = (zc*σ/E)2 = (2.576*30/15)² = 26.54 = 27
4. In a random sample of 26 computers, the mean repair cost was $130 with a sample
standard deviation of $36. Assume that the population is normally distributed a.Find the
margin of error for a 95% confidence interval. b.Find a 95% co
Since the population standard deviation is unknown, a Student’s t distribution with (n-1)
= (26-1) = 25 degrees of freedom is used to construct the confidence interval. The critical
value tc at a 95% confidence is 2.06
a) Margin of error, E = tc*s/√n = 2.06*36/√26 = 14.54
b) A 95% confidence interval for the mean repair cost is given by
(Xbar – E, Xbar + E) = (130 – 14.54, 130 + 14.54) = ($115.46, $144.54)