The weights of newborn baby boys born at a local hospital are believed to have a normal distribution with a mean weight of 3903 grams and a

Question

The weights of newborn baby boys born at a local hospital are believed to have a normal distribution with a mean weight of 3903 grams and a standard deviation of 446 grams. If a newborn baby boy born at the local hospital is randomly selected, find the probability that the weight will be less than 4884 grams. Round your answer to four decimal places.

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Minh Khuê 1 month 2021-08-07T20:29:41+00:00 1 Answers 2 views 0

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    2021-08-07T20:31:25+00:00

    Answer:

    0.9861 = 98.61% probability that the weight will be less than 4884 grams.

    Step-by-step explanation:

    Normal Probability Distribution:

    Problems of normal distributions can be solved using the z-score formula.

    In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

    Z = \frac{X - \mu}{\sigma}

    The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

    Mean weight of 3903 grams and a standard deviation of 446 grams.

    This means that \mu = 3903, \sigma = 446

    If a newborn baby boy born at the local hospital is randomly selected, find the probability that the weight will be less than 4884 grams.

    P-value of z when X = 4884. So

    Z = \frac{X - \mu}{\sigma}

    Z = \frac{4884 - 3903}{446}

    Z = 2.2

    Z = 2.2 has a p-value of 0.9861

    0.9861 = 98.61% probability that the weight will be less than 4884 grams.

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