Please help I don't understand it.

Question

please help I don't understand it. The average weight of a medium size egg is found to be 3.2 oz, with a standard deviation of 0.13 oz. What is the heaviest egg (to 2 decimal places) that we are 95% confident is still medium size? 3.2 oz 3.33 oz 3.45 oz 3.46 oz

Answer 1

The normal distribution tells us that 95.44% of all data lies within the region under the distribution curve centered at the mean (μ), and reaching back to Z_a = μ - 2σ and up to Z_b = μ + 2σ on the Z-score horizontal axis. 

 

Any score (data, weight of egg in ounces) not exceeding  μ +  2σ = 3.2 + 2(0.13) = 3.46 ounces is medium...i.e. mean weight + 2 standard deviations is the greatest weight of a medium size egg; beyond that, it's bigger.