Current learning objective: The Uniform Distribution Question 17 Score: 0 of 4 points Suppose that the value of a stock varies each day from $$ \$ 11.82 $$ to $$ \$ 16.17 $$ with a uniform distribution. Find the third quartile, i.e, $$ 75 \% $$ of all days the stock is below what value? $$ \$ $$ Enter your answer Round your answer to 2 decimal places.

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1. The value range is given by the interval $$[11.82,\, 16.17]$$ where the lower bound is $$a=11.82$$ and the upper bound is $$b=16.17$$.

2. For a uniform distribution, the $$p$$th quantile is given by:
   $$
   Q(p) = a + p(b - a)
   $$
   Here, $$p=0.75$$ for the third quartile.

3. Substitute the values:
   $$
   Q(0.75) = 11.82 + 0.75(16.17 - 11.82)
   $$

4. Calculate the difference:
   $$
   16.17 - 11.82 = 4.35
   $$

5. Multiply by 0.75:
   $$
   0.75 \times 4.35 = 3.2625
   $$

6. Add to the lower bound:
   $$
   11.82 + 3.2625 = 15.0825
   $$

7. Rounding to two decimal places, we obtain:
   $$
   15.08
   $$

Thus, the third quartile is $$\$15.08$$.
The third quartile is \$15.08.

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