Question

Production times are evenly distributed between 8 and 15.8 minutes and production times are never outside of this interval. What is the probability that a production time is between 9.7 and 12 minutes?

Answer 1

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.

$P(c \leq X \leq d) = \frac{d - c}{b-a}$

Production times are evenly distributed between 8 and 15.8 minutes and production times are never outside of this interval.

This means that $a = 8, b = 15.8$

What is the probability that a production time is between 9.7 and 12 minutes?

$d = 12, c = 9.7$.

So

$P(c \leq X \leq d) = \frac{d - c}{b-a}$

$P(9.7 \leq X \leq 12) = \frac{12 - 9.7}{15.8 - 8} = 0.2949$

29.49% probability that a production time is between 9.7 and 12 minutes