Final answer:
The probability that a single randomly selected well is less than 120 m deep is approximately 0.0668, and the probability that a single randomly selected well is between 100 m and 200 m deep is approximately 0.3190.
Step-by-step explanation:
To find the probability that a single randomly selected well is less than 120 m deep, we need to calculate the z-score and then use the standard normal distribution table. The formula for calculating the z-score is: z = (x - mean) / standard deviation. Substituting in the values from the given question, we get: z = (120 - 225) / 70 = -1.5. Referencing the standard normal distribution table, we find that the probability associated with a z-score of -1.5 is approximately 0.0668. Therefore, the probability that a single randomly selected well is less than 120 m deep is approximately 0.0668.
To find the probability that a single randomly selected well is between 100 m and 200 m deep, we need to calculate the z-scores for both values and find the area between those z-scores. The z-score for 100 m is: z = (100 - 225) / 70 = -1.786. The z-score for 200 m is: z = (200 - 225) / 70 = -0.357. Referring to the standard normal distribution table, we find the probabilities associated with these z-scores: approximately 0.0367 and 0.3557, respectively. To find the area between these two probabilities, we subtract the smaller probability from the larger probability: 0.3557 - 0.0367 = 0.3190. Therefore, the probability that a single randomly selected well is between 100 m and 200 m deep is approximately 0.3190.