Question

In the United States, birth weights are normally distributed, with a mean of 3420g and a standard deviation of 495g. If a hospital plans to establish special observation conditions for the 2% of babies less, what weight would be used to establish a cut-off point that separates 2% of the babies less heavy from the others?

Answer 1

Solution:-

Given that

In the United States, birth weights are normally distributed, with a mean of 3420g and a standard deviation of 495g. If a hospital plans to establish special observation conditions for the 2% of babies less

What weight would be used to establish a cut-off point that separates 2% of the babies less heavy from the others?

It is given that birth weights in United states is normally distributed with mean birth weight to be 3420 gram and standard deviation of birth weights to be 495 gram. Hospital is interested to set up for special observation conditions for the lightest 2% of babies. It is required to find the cut of that separates the lightest 2% from the rest of the birth weight.

From information given

Here, is population mean and is population standard deviation. The problem requires to find the cut-off birth weight by using the given information.

Thus, find the z-score associated with 2% or 0.02 and substitute it in the following formula to compute the raw score. The z score basically tells how many standard deviation one particular score is away from the mean.

Thus, the formula uses both mean and standard deviation. Use standard normal table and locate the area which is approximately 0.02. Then find the corresponding z score. The closest area is 0.0202

Thus, the z score is -2.05

Use the following formula to find the raw score

Here, x denotes the raw score. Substitute the given values in formula (1)

x = 2405

Thus, the answer is 2405 grams.

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