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17 September, 16:06

The number of violent crimes committed in a day possesses a distribution with a mean of 4.8 crimes per day and a standard deviation of 2 crimes per day. a random sample of 100 days was observed, and the sample mean number of crimes for the sample was calculated. describe the sampling distribution of the sample mean.

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  1. 17 September, 16:17
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    According to the central limit theorem (n> = 30), the sampling distribution of the sample mean is approximately normal with a mean of 4.8 and a standard deviation of 2.

    So:

    x = standard dev / sample size

    = 2 / 100

    = 1/50

    = 0.02; it is normal due to its large sample size
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