Answer :
To determine the probability that the class length is between 50.6 and 51.7 minutes, we can use the properties of a continuous uniform distribution.
A continuous uniform distribution is defined over an interval [tex][a, b][/tex], where each outcome within this interval is equally likely. For this question, the interval is [tex][50.0, 52.0][/tex] minutes.
The probability of an event in a continuous uniform distribution can be calculated using the formula:
[tex]P(a \leq X \leq b) = \frac{(c - d)}{(b - a)}[/tex]
where:
- [tex]a[/tex] is the minimum value of the uniform distribution (50.0 minutes).
- [tex]b[/tex] is the maximum value of the uniform distribution (52.0 minutes).
- [tex]c[/tex] is the lower bound of the interval of interest (50.6 minutes).
- [tex]d[/tex] is the upper bound of the interval of interest (51.7 minutes).
Plugging these values into the formula, we get:
[tex]P(50.6 \leq X \leq 51.7) = \frac{(51.7 - 50.6)}{(52.0 - 50.0)}[/tex]
[tex]P(50.6 \leq X \leq 51.7) = \frac{1.1}{2.0}[/tex]
[tex]P(50.6 \leq X \leq 51.7) = 0.55[/tex]
Therefore, the probability that a randomly selected class is between 50.6 and 51.7 minutes long is 0.5500 or 55.00%, rounded to four decimal places.
