Question

Let X be normally distributed with mean μ = 2,800 and standard deviation σ = 1,300. Find x such that P(X > x) = 0.025. (Round "z" value to 2 decimal places, and final answer to nearest whole number.)

Answer 1

To find 'x' such that P(X > x) = 0.025, we use the standard normal distribution. The corresponding 'x' value is approximately 2512.

Step-by-step explanation:

To find x such that P(X > x) = 0.025, we need to use the standard normal distribution. First, we convert the X distribution to the standard normal distribution (Z) using the formula Z = (X - μ) / σ, where μ is the mean and σ is the standard deviation. In this case, Z = (x - 2800) / 1300. Searching the Z-table, we find that the corresponding Z-value for a probability of 0.025 is approximately -1.96. Setting Z = -1.96 and solving for x, we get x = -1.96 * 1300 + 2800 = 2512. Using the rounding rules specified, x should be rounded to the nearest whole number, which gives x = 2512 as the final answer.