Final answer:
To find the probability that a single randomly selected value is between 219 and 227.9, we standardize the values using the z-score formula and look up corresponding probabilities in the standard normal distribution table. The probability is approximately 0.0381.
Step-by-step explanation:
To find the probability that a single randomly selected value is between 219 and 227.9, we need to calculate the area under the normal distribution curve between these two values. We can use the z-score formula to standardize the values and then look up the corresponding probabilities in the standard normal distribution table. The z-score for 219 is (219 - 213.5) / 84.5 = 0.065. The z-score for 227.9 is (227.9 - 213.5) / 84.5 = 0.170.
Using the standard normal distribution table, the probability corresponding to a z-score of 0.065 is 0.5260. The probability corresponding to a z-score of 0.170 is 0.5641. Now, to find the probability between these two values, we subtract the probability corresponding to a z-score of 0.065 from the probability corresponding to a z-score of 0.170: 0.5641 - 0.5260 = 0.0381.
Therefore, the probability that a single randomly selected value is between 219 and 227.9 is approximately 0.0381.