A machine is designed to fill 16-ounce bottes of shampoo. When the machine is working properly, the amount poured into the bottles follows a Normal distribution with mean 16.05 ounces and standard deviation 0.1 ounce. Assume the machine is working properly. If 4 bottles are randomly selected and the number of ounces in each bottle is measured, then there is a 95% probability the sample mean will fall in which of the following intervals? (a) 16.05 to 16.15 ounces (b) 16.00 to 16.10 ounces (c) 15.95 to 16.15 ounces (d) 15.90 to 16.20 ounces (e) 15.85 to 16.25 ounces

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Mathematics

Guest

28 February, 13:29

A machine is designed to fill 16-ounce bottes of shampoo. When the machine is working properly, the amount poured into the bottles follows a Normal distribution with mean 16.05 ounces and standard deviation 0.1 ounce. Assume the machine is working properly. If 4 bottles are randomly selected and the number of ounces in each bottle is measured, then there is a 95% probability the sample mean will fall in which of the following intervals? (a) 16.05 to 16.15 ounces (b) 16.00 to 16.10 ounces (c) 15.95 to 16.15 ounces (d) 15.90 to 16.20 ounces (e) 15.85 to 16.25 ounces

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Rudy Hart · Answer 1

(D) 15.90 to 16.20 ounces

Step-by-step explanation:

Confidence Interval = mean + or - (t*sd) / √n

Mean = 16.05 ounces, sd = 0.1 ounce, n = 4, degree of freedom = n - 1 = 4 - 1 = 3, t = 3.182

Lower limit = 16.05 - (3.182*0.1) / √4 = 16.05 - 0.15 = 15.90 ounces

Upper limit = 16.05 + (3.182*0.1) / √4 = 16.05 + 0.15 = 16.20 ounces

The sample mean will fall from 15.90 to 16.20 ounces