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The probability of a randomly chosen woman taller than 65 inches is 0.5
Step-by-step explanation:
To find the probability of a random variable X which has a normal distribution do that
- If X > b, find the z-score using the formula z = (b - μ)/σ, where μ is the mean and σ is the standard deviation
- Use the normal distribution table of z to find the corresponding area to the right of z-score (Area to the right = 1 - area to the left)
∵ The heights of adult women are normally distributed with
μ = 65 inches
∵ σ = 2.5 inches
- We need to find the probability of the woman taller than 65 inches
∵ X > 65
∴ b = 65
- Find z-score
∵
- Use the normal distribution table to find the area corresponding to z
∵ The corresponding area of z = 0 is 0.5
- Area to the right = 1 - area to the left
∴ P(x > 65) = 1 - 0.5 = 0.5
The probability of a randomly chosen woman taller than 65 inches is 0.5
Learn more:
You can learn more about the probability in brainly.com/question/4625002
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