Let us revisit the commute times example and calculate the $x$-value when given the probability of at least $x$.

Example 36.1.1

Problem Setup: During the morning commute, the time it takes to drive to BCIT follows a uniform distribution and is between 30 and 55 minutes.

Question: 50% of the time it takes you at least how long to get to campus?

You Try: Let us first determine the values to input in the equation below:

$$P(x_1 \le x \le x_2) = \frac{x_2-x_1}{b-a} = p$$

Solution: Now, use algebra to solve for the minimum time it takes you half of the time to get to campus. Select your answer from the options below:

Let us now change up the problem slightly and show the solution in a video (see below).

Example 36.1.2

Problem Setup: Let us continue on with the previous example:

• Your commute times follow a uniform distribution
• And are between 30 and 55 minutes.

Question: 30% of the time, it takes you less than how many minutes to get to campus? Solve the problem by hand.

Solution: Click here to download the written solutions. Also, see the video below:

Let us finish up this section by going through how to use Excel’s Goal Seek to solve the previous example (see below).

Example 36.1.3

Problem Setup: Let us continue on with the previous example:

• Your commute times follow a uniform distribution
• And are between 30 and 55 minutes.

Question: 30% of the time, it takes you less than how many minutes to get to campus? Solve the problem using Excel’s Goal Seek.

Solution: Click here to download the Excel solutions shown in the solution video below:

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