The weights of newborn baby boys born at a local hospital are believed to have a normal distribution with a mean weight of 4016 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 4016 grams and a standard deviation of 532 grams. If a newborn baby boy born at the local hospital is randomly selected, find the probability that the weight will be less than 5026 grams. Round your answer to four decimal places.

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Audrey 1 month 2021-10-14T20:29:11+00:00 1 Answer 0 views 0

Answers ( )

  1. Charlotte
    0
    2021-10-14T20:31:10+00:00

    Answer:

    Required Probability = 0.97062

    Step-by-step explanation:

    We are given that the weights of newborn baby boys born at a local hospital are believed to have a normal distribution with a mean weight of 4016 grams and a standard deviation of 532 grams.

    Let X = weight of the newborn baby, so X ~ N(\mu=4016 , \sigma^{2} = 532^{2})

    The standard normal z distribution is given by;

                  Z = \frac{X-\mu}{\sigma} ~ N(0,1)

    Now, probability that the weight will be less than 5026 grams = P(X < 5026)

    P(X < 5026) = P( \frac{X-\mu}{\sigma} < \frac{5026-4016}{532} ) = P(Z < 1.89) = 0.97062

    Therefore, the probability that the weight will be less than 5026 grams is 0.97062 .

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