Question 1195186
The mean of the sampling distribution of n=9 is still 2.63 inches. The sd is 0.03/sqrt(9) or 0.01 inch.
The probability of the sample mean < 2.61 inches is (2.61-2.63)/0.01=z and z <=-2. This has probability of 0.0228.
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Between 2.62 and 2.64 inches is z between -1 and +1 with probability of 0.6836
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z(0.2)=-0.8416 and z(0.8)=0.8416
so z=(x-mean)/sd
0.8416=(x-2.63)/0.01
0.08416=x-2.63
x=2.638 inches for the upper limit
x=2.546 inches for the lower limit
Those two values enclose the sample mean symmetrically.