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Answer:
95% two-sided confidence interval on the true mean breaking strength is (94.8cm, 99.2cm)
Step-by-step explanation:
Our sample size is 11.
The first step to solve this problem is finding our degrees of freedom, that is, the sample size subtracted by 1. So
.
Then, we need to subtract one by the confidence level
and divide by 2. So:

Now, we need our answers from both steps above to find a value T in the t-distribution table. So, with 10 and 0.025 in the two-sided t-distribution table, we have 
Now, we find the standard deviation of the sample. This is the division of the standard deviation by the square root of the sample size. So

Now, we multiply T and s
cm
For the upper end of the interval, we add the sample mean and M. So the upper end of the interval here is
cm
So
95% two-sided confidence interval on the true mean breaking strength is (94.8cm, 99.2cm).
Given

We have to set the restraint

because a square root is non-negative, and thus it can't equal a negative number. With this in mind, we can square both sides:

The solutions to this equation are 7 and -2. Recalling that we can only accept solutions greater than or equal to -1, 7 is a feasible solution, while -2 is extraneous.
Similarly, we have

So, we have to impose

Squaring both sides, we have

The solutions to this equation are 5 and 10. Since we only accept solutions greater than or equal to 7, 10 is a feasible solution, while 5 is extraneous.