1. A study on the duration of tires (in kilometers traveled and tested under laboratory conditions), indicates that this follows a normal distribution, with a mean of 45,000 km and a standard deviation of 2,000 km. Based on this information, determine:

a) The probability that a randomly selected tire will last between 43,000 and 47,000 km.

b) The probability that a tire with a duration greater than 46,500 km is chosen.

c) The minimum duration of 87.49% of the tires with the longest duration.

2. In a laboratory culture, it is observed that, on average, an abnormal bacterium appears every 20 minutes.

a) What is the probability that an abnormal bacterium will appear in at least one hour?

b) What is the probability that an abnormal bacterium will be found within the first 45 minutes?

3. The sales volume of a store is uniformly distributed between 35 and 110 million pesos.

Certain:

a) The probability that sales are less than 85 million.

b) The probability that sales are greater than 100 million.

c) What is the expected sales volume?