Final answer:
The median of the normal distribution with μ = 100 and σ = 20 is 100. P(x ≥ median) = 0.5 and P(x ≤ 75) = 0.1056.
Step-by-step explanation:
The median of a normal distribution can be found by using the formula Median = Mean. In this case, the mean is μ = 100, so the median is also 100.
To find P(x ≥ median), we need to find the area to the right of the median. Since the distribution is symmetric, the area to the right of the median is equal to the area to the left of the median. So P(x ≥ median) = 0.5.
To find P(x ≤ 75), we need to find the area to the left of 75. We can convert this value to a z-score by using the formula z = (x - μ) / σ, where x is the given value, μ is the mean, and σ is the standard deviation. So, z = (75 - 100) / 20 = -1.25. Using a z-table, we can find that the area to the left of -1.25 is approximately 0.1056. Therefore, P(x ≤ 75) = 0.1056.