Suppose a player's true batting average is Normal, with mu = .273, and standard deviation, sigma = 0.02. What is the probability that this player will have a batting average GREATER THAN 0.300 on the basis of luck alone

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Suppose a player's true batting average is Normal, with mu = .273, and standard deviation, sigma = 0.02. What is the probability that this player will have a batting average GREATER THAN 0.300 on the basis of luck alone? 

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Step 1

It is given that the players true batting average is normally distributed with mean 0.273 and standard deviation 0.02.

Denote the random variable X as the batting average of a randomly selected player.

That is, µ= 0.273, σ = 0.02.

Thus, X~ N (0.273, 0.02).

 

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