Final answer:
To find the probability of selecting someone who is taller than 115 inches followed by someone who is shorter than 102 inches, first, we calculate the z-score for each height using the formula z = (x - mean) / standard deviation. Then, we look up the probability from the standard normal distribution table using the z-scores. Finally, we multiply the probabilities together to find the overall probability.
Step-by-step explanation:
To find the probability of selecting someone who is taller than 115 inches followed by someone who is shorter than 102 inches, we need to find the probability of each event separately and then multiply them together.
First, we calculate the z-score for a height of 115 inches using the formula z = (x - μ) / σ. Plugging in the values, we get z = (115 - 75) / 10 = 4.
Looking up the z-score of 4 in the standard normal distribution table, we find that the probability of selecting someone taller than 115 inches is approximately 0.9999683 (rounded to 7 decimal places).
Next, we calculate the z-score for a height of 102 inches using the same formula. Plugging in the values, we get z = (102 - 75) / 10 = 2.7.
Looking up the z-score of 2.7 in the standard normal distribution table, we find that the probability of selecting someone shorter than 102 inches is approximately 0.9964057 (rounded to 7 decimal places).
Finally, we multiply the probabilities together to find the probability of both events occurring: 0.9999683 * 0.9964057 = 0.9963782 (rounded to 7 decimal places).
Therefore, the probability of selecting someone who is taller than 115 inches followed by someone who is shorter than 102 inches is approximately 0.9963782.