Final answer:
To find the probability P(x<80), convert the value to a Z-score and use a Z-table to find the area to the left of the Z-score. The probability is approximately 30.85%.
Step-by-step explanation:
To find the probability P(x<80), we need to standardize the value of 80 using the Z-score formula. The Z-score is calculated by subtracting the mean from the value and dividing by the standard deviation. In this case, the Z-score is calculated as (80 - 82) / 4 = -0.5. We can then use a Z-table or a calculator to find the area to the left of the Z-score.
Looking up the Z-score -0.5 in a Z-table, we find that the area to the left of the Z-score is approximately 0.3085. Therefore, the probability P(x<80) is approximately 0.3085 or 30.85%.