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(3) The container for a chinchilla dust bath should be filled to a depth of 2.2 One chinchilla owner fills her dust bath to a mean depth of 2.1 with a standard deviation of .4. What is the probability that the average depth of the next 24 baths the chinchilla gets is between 2 and 2.25?

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Answer #1

Note that sample mean X follows a Normal distribution with Mean μ 2.1 Standard deviation-o/vn :0.0816 Note that z (-/(o/Nn) -(x-2.1)/0.0816 (Eq.1) follows standard Normal. When X- 2, from (Eq.1),z-1.23 When X- 2.25, from (Eq.1),z 1.84 P(2-X-2.25)-P(-1.23-Z < 1.84-P(Z < 1.84)-P(Ζ <-1.23-09671-0.1093-0.8578 (ans)

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