Kelley Collins
01/26/2023 · Senior High School
b) Suppose that the time it takes a data collection operator to fill out an electronic form for a database is uniformly between 1.5 and 2.2 minutes i. What is the probability that it will take less than two minutes to fill out the form? ii. Determine the cumulative distribution function of the time it takes to fill out the form
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**Part b.i: Probability that it takes less than 2 minutes**
The probability is \( \frac{5}{7} \) (approximately 71.43 %).
**Part b.ii: Cumulative Distribution Function (CDF)**
\[
F_X(x) =
\begin{cases}
0 & \text{if } x < 1.5, \\
\frac{x - 1.5}{0.7} & \text{if } 1.5 \leq x \leq 2.2, \\
1 & \text{if } x > 2.2.
\end{cases}
\]
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