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?
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability (±.025) and its Z score.
95% = mean ± Z (SD)
Consider only positive value.
To find the heaviest egg that we are 95% confident is still medium-sized, we need to use the concept of confidence intervals.
A confidence interval is a range of values within which we can be confident that the true population parameter lies. In this case, we want to find the upper limit of the confidence interval for the weight of a medium-sized egg.
To calculate the confidence interval, we can use the formula:
Upper Limit = Mean + (Z * Standard Deviation)
Where:
- Mean is the average weight of a medium size egg (3.2 oz)
- Z is the Z-score corresponding to the desired confidence level (in this case, 95% confidence level)
- Standard Deviation is the standard deviation of the weight of medium-sized eggs (0.13 oz)
Since we want a 95% confidence level, we need to find the Z-score associated with it. The Z-score can be found using a Z-table or calculated using statistical software.
Looking up the Z-score of 95% confidence level, the Z-score is approximately 1.96.
Now we can substitute the values into the formula:
Upper Limit = 3.2 + (1.96 * 0.13)
Calculating this expression:
Upper Limit ≈ 3.2 + (1.96 * 0.13)
Upper Limit ≈ 3.2 + 0.2548
Rounded to 2 decimal places:
Upper Limit ≈ 3.45
Therefore, the heaviest egg (to 2 decimal places) that we are 95% confident is still medium-sized is approximately 3.45 oz.