A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 47.0 and 57.0 minutes. Find the probability that a given class period runs between 51.25 and 51.75 minutes.
Find the probability of selecting a class that runs between 51.25 and 51.75 minutes.
(Round to three decimal places as needed.)
Answer
Final Answer: The probability that a given class period runs between 51.25 and 51.75 minutes is \(\boxed{0.05}\) or \(\boxed{5\%}\).
Step 1 ：The problem is asking for the probability that a class period runs between 51.25 and 51.75 minutes. Since the lengths of her classes are uniformly distributed between 47.0 and 57.0 minutes, the total range of time is 57.0 - 47.0 = 10.0 minutes.
Step 2 ：The range of time we are interested in is 51.75 - 51.25 = 0.5 minutes.
Step 3 ：The probability of a class running between 51.25 and 51.75 minutes is therefore \(\frac{0.5}{10.0} = 0.05\) or 5%.
Step 4 ：Final Answer: The probability that a given class period runs between 51.25 and 51.75 minutes is \(\boxed{0.05}\) or \(\boxed{5\%}\).
