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A population of values has a normal distribution with μ=208.5 and σ=35.4. You intend to draw a random sample of size n=236.

Find the probability that a single randomly selected value is greater than 203.4.

User Joninx
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Final answer:

The probability that a single randomly selected value is greater than 203.4 is approximately 55.62%.

Step-by-step explanation:

To find the probability that a single randomly selected value is greater than 203.4, we need to calculate the z-score and then find the area under the standard normal curve.

The formula for z-score is (x - μ) / σ, where x is the value, μ is the population mean, and σ is the population standard deviation. In this case, the z-score is

(203.4 - 208.5) / 35.4 ≈ -0.1441.

Looking up this z-score in the z-table, we find that the area to the left of this z-score is 0.4438.

Since we want the probability that the value is greater than 203.4, we subtract this area from 1 to get the probability that a single randomly selected value is greater than 203.4, which is approximately 1 - 0.4438 = 0.5562, or 55.62%.

User Phortx
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