Final answer:
To find the probability P(X < 47.9) from a normal distribution with a mean of 115.7 and a standard deviation of 21.2, we calculate the z-score for x = 47.9 and find the probability associated with it using a standard normal distribution table or calculator. The probability is almost zero, indicating that it is highly unlikely for a randomly selected value to be less than 47.9.
Step-by-step explanation:
To find the probability P(X < 47.9), which represents the probability of a randomly selected value being less than 47.9, we need to standardize the value using the mean and standard deviation. The formula to standardize a value is: z = (x - mean) / standard deviation. Using this formula, we can calculate the z-score for x = 47.9. z = (47.9 - 115.7) / 21.2 = -3.5877.
Next, we can use a standard normal distribution table or calculator to find the probability associated with the z-score of -3.5877. The probability calculated is nearly zero, indicating that it is extremely unlikely for a randomly selected value to be less than 47.9 in this normal distribution.