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The weights of newborn baby boys born at a local hospital are believed to have a normal distribution with a mean weight of 3958 grams and a standard deviation of 362 grams. If a newborn baby boy born at the local hospital is randomly selected, find the probability that the weight will be less than 4320 grams. Round your answer to four decimal places.

Respuesta :

pedrocarratore

Answer:

0.8413 or 84.13%

Step-by-step explanation:

The difference from 4320 grams from the mean is:

[tex]d=4320-3958=362\ grams[/tex]

This is exactly 1 standard deviation.

According to the empirical rule, 68.26% of all data is within 1 standard deviation of the mean, which means that 34.13% of all data is within the mean and 1 standard deviation over the mean. We also know that the mean is at the 50th percent of the normal distribution.

Therefore, the probability that the weight will be less than 4320 grams is:

[tex]P(X\leq 4320) = 0.50+0.3413=0.8413 = 84.13\%[/tex]

The probability is 0.8413 or 84.13%