In a random sample of 65 bolts, the mean length was 1.77 inches and the standard

Question

In a random sample of 65 bolts, the mean length was 1.77 inches and the standard deviation was 0.07 inch. Use a normal distribution or a t distribution to construct a 95% confidence interval for the mean. Which distribution should be used to construct the 95% confidence interval? A. Use a t-distribution because n greaterthanorequalto 30. B. Use a normal distribution because n greaterthanorequalto 30. C. Use a normal distribution because the lengths are normally distributed and a is known. D. Use a t-distribution because the lengths are normally distributed and sigma is known. The 95% confidence interval is ()

Explanation / Answer

Sample size n = 65 bolts

Mean length xbar= 1.77 inches

standard deviation s = 0.07 inch

Here option B is correct. as n >=30.

In this population standard deviation is unknown so option C is incorrect.

95% confidence interval = xbar+- Z95% (s/n)

= 1.77 +- 1.96 * (0.07/ 65)

= 1.77 +- 1.96 * 0.008682

= (1.75, 1.79)

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