A company making refrigerators strives for the internal temperature to have a mean of 37.5 degrees with a population standard deviation of 0.6 degrees, based on samples of 100. A sample of 100 refrigerators have an average temperature of 37.48 degrees. Are the refrigerators within the 90% confidence interval? a. No, the temperature is outside the confidence interval of (37.40, 37.60) b. No, the temperature is outside the confidence interval of (36.90, 38.10) c. Yes, the temperature is within the confidence interval of (37.40, 37.60) d. Yes, the temperature is within the confidence interval of (36.90, 38.10)

Question

Mathematics

Eliana Gilbert

20 November, 19:00

A company making refrigerators strives for the internal temperature to have a mean of 37.5 degrees with a population standard deviation of 0.6 degrees, based on samples of 100. A sample of 100 refrigerators have an average temperature of 37.48 degrees. Are the refrigerators within the 90% confidence interval? a. No, the temperature is outside the confidence interval of (37.40, 37.60) b. No, the temperature is outside the confidence interval of (36.90, 38.10) c. Yes, the temperature is within the confidence interval of (37.40, 37.60) d. Yes, the temperature is within the confidence interval of (36.90, 38.10)

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Answers (1)

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Keagan Brady · Answer 1

Yes, the temperature is within the confidence interval (37.40, 37.60)

Step-by-step explanation:

Mean=37.48, sd=0.6, n=100, df=n-1=100-1=99, t value corresponding to 99 degrees of freedom and 90% confidence interval is 1.6602

CI = (mean + or - t*sd/√n)

CI = (37.48 + 1.6602*0.6/√100) = 37.48 + 0.0996 = 37.60

CI = (37.48 - 1.6602*0.6/√100) = 37.48 - 0.0996 = 37.40

CI is (37.40, 37.60)