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2 July, 21:06

The rent for a one-bedroom apartment in Southern California follows the normal distribution with a mean of $2,200 per month and a standard deviation of $250 per month. The distribution of the monthly costs does not follow the normal distribution. In fact, it is positively skewed. What is the probability of selecting a sample of 50 one bedroom apartments and finding the mean to be at least $1,950 per month?

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  1. 2 July, 21:33
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    The probability is 1.

    Explanation:

    Despite that the he distribution is positively skewed, the distribution of sample means of one-bedroom apartments will still be a a normal distribution based on Central Limit Theorem.

    Since we have

    μ = mean = 2200

    SD = standard deviation = 250

    n = sample size = 50

    Therefore,

    Standard error = SD : √n

    = 250 : √50

    = 250 : 7.07106781186548

    = 35.3553390593274 approximately 35.36

    Standardize xbar to z = (xbar - μ) : (SD : √n)

    Therefore, we have:

    P (xbar > 1,950) = P (z > (1,950 - 2200) : 35.36)

    = P (z > - 250 : 35.36)

    = P (z > - 7.07) = 1

    Therefore, the probability of selecting a sample of 50 one bedroom apartments is 1 which can be said to be certain.
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