D = 8cm H=8cm - Gauthmath

Math Resources/Statistics/

Question

The weights of newborn baby boys born at a local hospital are believed to have a normal distribution with a mean weight of 3415 grams and a  variance of 136,161. If a newborn baby boy born at the local hospital is randomly selected, find the probability that the weight will be less than 3669 grams. Round your answer to four decimal places.SHOW LESS3

Solution

The probability that a newborn baby boy will weigh less than 3669 grams is approximately 0.7549.

Step 1: Calculate the standard deviation (σσ). σ=√(136,161)=369gramsσ = √(136,161) = 369 grams

Step 2: Calculate the z-score for x=3669gramsx = 3669 grams. z=(3669−3415)/369≈0.6892z = (3669 - 3415) / 369 ≈ 0.6892

Step 3: Find the area to the left of z=0.6892z = 0.6892 using a standard normal distribution table or calculator. Area≈0.7549Area ≈ 0.7549

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