A random sample of 30 varieties of cereal was selected. The average number of calories per serving for these cereals is x-120. Assuming that σ = 10, find a 95% confidence interval for the mean number of calories, μ, in a serving of cereal. a. 115.30 to 124.70 b. 116.42 to 123.58 c. 118.00 to 122.00 d. 117.00 to 123.00

Question

Mathematics

Sheldon Crosby

6 September, 06:03

A random sample of 30 varieties of cereal was selected. The average number of calories per serving for these cereals is x-120. Assuming that σ = 10, find a 95% confidence interval for the mean number of calories, μ, in a serving of cereal. a. 115.30 to 124.70 b. 116.42 to 123.58 c. 118.00 to 122.00 d. 117.00 to 123.00

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Abigail Norman · Answer 1

Answer: confidence interval = b. (116.42 to 123.58)

Step-by-step explanation:

Given;

Number of samples n = 30

Standard deviation r = 10

Mean x = 120

Confidence interval of 95%

Z' = t (0.025) = 1.96

Confidence interval = x + / - Z' (r/√n)

= 120 + / - 1.96 (10/√30)

= 120 + / - 3.58

= (116.42, 123.58)