An appliance manufacturer gives a warranty, and 95 percent of its appliances do not require repair before the warranty expires. An organization buys 10 of these appliances. Calculate an interval that contains 95.44 percent of all the appliances that will not require repair.

A. [8.12, 10.88]

B. [7.43, 11.57]

C. [8.81, 10.19]

D. [8.55, 10.45]

Question

Charlotte Miles

Mathematics

5 February, 17:18

An appliance manufacturer gives a warranty, and 95 percent of its appliances do not require repair before the warranty expires. An organization buys 10 of these appliances. Calculate an interval that contains 95.44 percent of all the appliances that will not require repair.

A. [8.12, 10.88]

B. [7.43, 11.57]

C. [8.81, 10.19]

D. [8.55, 10.45]

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Answers (1)

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Libby · Answer 1

An appliance manufacturer gives a warranty, and 95 percent of its appliances do not require repair before the warranty expires. An organization buys 10 of these appliances. Calculate an interval that contains 95.44 percent of all the appliances that will not require repair.

A. [8.12, 10.88]

B. [7.43, 11.57]

C. [8.81, 10.19]

D. [8.55, 10.45]

Step-by-step explanation:

We can calculate the confidence interval for a proportion p = 0.95 and a sample size n = 10.

Note that the critical value for 95.44% confidence is 1.9991. Z-score table.

Between 81.22% and 108.78% of 10 units is 8.12 and 10.88 units. Therefore the confidence interval is: (8.12, 10.88).

Answer: [ 8.12, 10.88 ]