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The random variable X represents the house rent price in Istanbul. It has a mean of 5000 TL and a standard deviation of 400 TL.

The random variable X represents the house rent price in Istanbul. It has a mean of 5000 TL and a standard deviation of 400 TL. A random sample of 36 rent houses is taken from Istanbul. It is assumed that the distribution x is the sample mean of rent prices in Istanbul.

(a) What is the probability that the sample mean falls between 4800 TL and 5200 TL?

(b) What is the sample size n in order to have P(4900 < x < 5100) = 0.99

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