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.
Find the 80th percentile score for these weights.
To find the 80th percentile score for the weights of male babies less than 2 months old, we can use the standard normal distribution table or a statistical calculator.
Step 1: Standardize the value
First, we need to standardize the score using the Z-score formula:
Z = (X - μ) / σ
Where:
Z is the standardized value
X is the value we want to standardize
μ is the mean of the distribution
σ is the standard deviation of the distribution
In this case, X is the 80th percentile, μ is 11.5 pounds, and σ is 2.7 pounds.
Step 2: Find the Z-score
Now, we need to find the Z-score associated with the 80th percentile using the standard normal distribution table or a statistical calculator.
The Z-score associated with the 80th percentile is approximately 0.8416.
Step 3: Compute the actual value
Finally, we can compute the actual value by rearranging the formula:
X = Z * σ + μ
Substituting in the values, we have:
X = 0.8416 * 2.7 + 11.5
Calculating this, we get:
X ≈ 14.274
Therefore, the 80th percentile score for the weights of male babies less than 2 months old is approximately 14.274 pounds.
To find the 80th percentile score for these weights, we need to use the Z-score formula and the standard normal distribution table.
The Z-score formula is given by:
Z = (X - μ) / σ
Where:
Z is the Z-score
X is the value we want to find the percentile for
μ is the mean of the distribution
σ is the standard deviation of the distribution
In this case, X is the weight we want to find the 80th percentile for, μ is the mean of 11.5 pounds, and σ is the standard deviation of 2.7 pounds.
To find the Z-score corresponding to the 80th percentile, we can use the standard normal distribution table or a calculator. The 80th percentile corresponds to a Z-score of approximately 0.84.
Now we can rearrange the Z-score formula to solve for X:
Z = (X - μ) / σ
Multiply both sides by σ:
Z * σ = X - μ
Add μ to both sides:
X = Z * σ + μ
Substituting the values, we get:
X = 0.84 * 2.7 + 11.5
Calculating this, we find:
X ≈ 13.028
Therefore, the 80th percentile score for these weights of male babies less than 2 months old in the United States is approximately 13.028 pounds.
Try z-scores:
z = (x - mean)/sd
Substitute the data into the above formula and solve for x.
mean = 11.5
sd = 2.7
z = score from the table
Use the table to find z-score at the 80th percentile.
I'll let you take it from here.