Answer:
29.49% probability that a production time is between 9.7 and 12 minutes
Step-by-step explanation:
An uniform probability is a case of probability in which each outcome is equally as likely.
For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.
The probability that we find a value X between c and d, in which d is greater than c, is given by the following formula.
[tex]P(c \leq X \leq d) = \frac{d - c}{b-a}[/tex]
Production times are evenly distributed between 8 and 15.8 minutes and production times are never outside of this interval.
This means that [tex]a = 8, b = 15.8[/tex]
What is the probability that a production time is between 9.7 and 12 minutes?
[tex]d = 12, c = 9.7[/tex].
So
[tex]P(c \leq X \leq d) = \frac{d - c}{b-a}[/tex]
[tex]P(9.7 \leq X \leq 12) = \frac{12 - 9.7}{15.8 - 8} = 0.2949[/tex]
29.49% probability that a production time is between 9.7 and 12 minutes
