The weights of male babies less than 2 months old in the United States is normally distributed with a mean of 11.5 pounds and a standard deviation of 2.7 pounds.
How do I find the 80th percentile for these weights?
To find the 80th percentile for the weights of male babies less than 2 months old, you can use the cumulative distribution function (CDF) of the normal distribution. The CDF gives you the probability that a randomly selected weight is less than or equal to a given value.
Step 1: Standardize the value.
To use the CDF function, you need to standardize the desired percentile using the mean and standard deviation. The formula for standardization is:
Z = (X - μ) / σ
where Z is the standardized value, X is the desired percentile, μ is the mean, and σ is the standard deviation.
In this case, you want to find the value that corresponds to the 80th percentile, so X = 80.
Step 2: Use the CDF function.
Use the standardized value to calculate the probability of being less than or equal to that value using the CDF function of the standard normal distribution. This can be done using statistical software or a calculator with a normal distribution function.
Step 3: Convert back to the original scale.
Finally, convert the probability obtained from step 2 back into the original scale by multiplying it by the standard deviation and adding it to the mean.
P(Z ≤ X) = P(X ≤ Z) = 0.80
Using this information, you can find the value corresponding to the 80th percentile for the weights of male babies less than 2 months old in the United States.
Look up in your Z table for the upper tail at 20%
You can play around with this at
http://davidmlane.com/hyperstat/z_table.html
where you can set the mean and variance and explore various properties of the normal distribution