The weights of newborn baby boys born at a local hospital are believed to have a normal distribution with a mean weight of 36843684 grams and a standard deviation of 448448 grams. If a newborn baby boy born at the local hospital is randomly selected, find the probability that the weight will be less than 43564356 grams. Round your answer to four decimal places.

Question

agentjean2867 agentjean2867

12-03-2020
Mathematics

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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 36843684 grams and a standard deviation of 448448 grams. If a newborn baby boy born at the local hospital is randomly selected, find the probability that the weight will be less than 43564356 grams. Round your answer to four decimal places.

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joaobezerra joaobezerra · Answer 1 · 2020-03-17T00:18:48+01:00

Answer:

93.32% probability that the weight will be less than 4356 grams.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

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 pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

[tex]\mu = 3684, \sigma = 448[/tex]

If a newborn baby boy born at the local hospital is randomly selected, find the probability that the weight will be less than 4356 grams.

This is the pvalue of Z when X = 4356. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{4356 - 3684}{448}[/tex]

[tex]Z = 1.5[/tex]

[tex]Z = 1.5[/tex] has a pvalue of 0.9332

93.32% probability that the weight will be less than 4356 grams.