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

To find the probability that it will take less than two minutes to fill out the form, we can use the properties of a uniform distribution. The range of time is from 1.5 minutes to 2.2 minutes. The total length of this interval is: 2.2 - 1.5 = 0.7 minutes. Now, we want to find the probability that the time (X) is less than 2 minutes: P(X < 2) = (2.0 - 1.5) / (2.2 - 1.5) = 0.5 / 0.7 ≈ 0.7143. So, the probability that it will take less than two minutes is approximately 0.7143 or 71.43%. Now, for the cumulative distribution function (CDF) of the time it takes to fill out the form, we can define it as follows: - For x < 1.5, F(x) = 0 (since the time cannot be less than 1.5 minutes). - For 1.5 ≤ x < 2.2, F(x) = (x - 1.5) / (2.2 - 1.5). - For x ≥ 2.2, F(x) = 1 (since the time cannot exceed 2.2 minutes). Thus, the CDF of the time to fill out the form is: F(x) = 0 for x < 1.5, (x - 1.5) / 0.7 for 1.5 ≤ x < 2.2, 1 for x ≥ 2.2.