Final answer:
To find the probability that a randomly selected value is less than -77.3 in a normal distribution with a mean of 31.1 and standard deviation of 51.6, we need to calculate the z-score, which is -1.956. The probability associated with this z-score is approximately 0.0256, or 2.56%.
Step-by-step explanation:
To find the probability that a randomly selected value is less than -77.3 in a normal distribution with a mean of 31.1 and standard deviation of 51.6, we need to calculate the z-score first.
The z-score formula is: z = (x - µ) / σ, where z is the z-score, x is the value, µ is the mean, and σ is the standard deviation.
So, in this case, the z-score is: z = (-77.3 - 31.1) / 51.6 = -1.956.
To find the probability associated with this z-score, we can use a standard normal distribution table or a calculator. Looking up -1.956 in a table or using a calculator, we find that the probability is approximately 0.0256, or 2.56%.