Questions: Suppose that the value of a stock varies each day from 9.82 to 24.17 with a uniform distribution. Find the upper quartile; 25% of all days the stock is above what value? (Enter your answer to the nearest cent.)

Suppose that the value of a stock varies each day from 9.82 to 24.17 with a uniform distribution.

Find the upper quartile; 25% of all days the stock is above what value? (Enter your answer to the nearest cent.)

Transcript text: Suppose that the value of a stock varies each day from $\$ 9.82$ to $\$ 24.17$ with a uniform distribution. Find the upper quartile; 25\% of all days the stock is above what value? (Enter your answer to the nearest cent.) \$

Solution

Solution Steps

Step 1: Calculate the Range

To find the third quartile of a stock's value with a uniform distribution, we first calculate the range of the stock's daily variation. The range $R$ is the difference between the upper bound $U$ and the lower bound $L$, which is $R = U - L = 24.17 - 9.82 = 14.350$.

Step 2: Determine the Third Quartile Position

Since the distribution is uniform, the third quartile $Q3$ is located at 75% of the range from the lower bound. This can be calculated as $Q3 = L + 0.75 \times R = 9.82 + 0.75 \times 14.350 = 20.583$.

Step 3: Round the Result

The calculated value of the third quartile is rounded to the nearest cent (or specified decimal places) to match the format of the question. Thus, $Q3$ rounded is 20.58.