Final answer:
To find the value of x that 10% of measurements exceed, the 90th percentile z-score (1.28) is used and the equation 1.28 = (x - 50) / 10 is solved, resulting in x = 62.8.
Step-by-step explanation:
To determine the value of x which 10% of the measurements will exceed given a mean of 50 and a standard deviation of 10, we need to use the concept of the z-score in a normal distribution. First, we find the z-score that corresponds to the 90th percentile because 100% - 10% = 90%. This means we want the z-score where 90% of the data falls below it. You can use a z-table or a calculator to find this, and you will find that the z-score for the 90th percentile is approximately 1.28.
Next, we apply the z-score formula:
Z = (x - mean) / standard deviation
Here, we plug in the z-score (1.28), the mean (50), and the standard deviation (10), and solve for x:
1.28 = (x - 50) / 10
x - 50 = 12.8
x = 62.8
Therefore, the value of x which 10% of the measurements exceed is approximately 62.8.