Final answer:
To find the probability P(x ≤ 60) for a normal variable with mean 49 and standard deviation 6.9, calculate the z-score for x = 60 and use a standard normal distribution table or calculator to find the associated probability.
Step-by-step explanation:
To find the probability P(x ≤ 60), we need to calculate the area under the normal distribution curve up to the value of 60.
Since the given variable x is normally distributed with a mean of 49 and a standard deviation of 6.9, we can find the z-score for x = 60 using the formula:
z = (x - mean) / standard deviation
Substituting the values, we get:
z = (60 - 49) / 6.9 = 1.59
Now, we can use a standard normal distribution table or a calculator to find the probability associated with the z-score of 1.59. The probability P(x ≤ 60) is equivalent to the probability of z ≤ 1.59.
Using a standard normal distribution table or calculator, we find that the probability P(x ≤ 60) is approximately 0.9441, or 94.41%.