It is known that the birth weights of full-term newborn infants in the U.S. ha

Question

It is known that the birth weights of full-term newborn infants in the U.S. have an approximately normal distribution with a mean weight of 6.8 lbs and a standard deviation of 1.7 lbs.

Find the range of weights that the middle 90% lies between?

Enter the answer as interval ( , )

Round to 2 decimal places.

Answer 1

90% in the middle of the normal distribution means 5% on one side of the tail (from a table or technology, z = 1.645)

The range is from -z to +z which is 2z

The actual interval is derived from z = (x- μ)/σ

x = μ + zσ or from 6.8 - 1.7z to 6.8 + 1.7z where z = 1.645

The range = 2(1.7)z

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