People's heights are normally distributed, with a mean of 170cm and standard deviation of 10cm. What is the 10th percentile of people's heights (in cm).Please round your result to one decimal place.Note that from the z-distribution table, we know:P(Z<= -1.645) = 5%P(Z<= -1.96) = 2.5%P(Z<= -1.28) = 10%
Question
People's heights are normally distributed, with a mean of 170cm and standard deviation of 10cm. What is the 10th percentile of people's heights (in cm).Please round your result to one decimal place.Note that from the z-distribution table, we know:P(Z<= -1.645) = 5%P(Z<= -1.96) = 2.5%P(Z<= -1.28) = 10%
Solution
To find the 10th percentile of people's heights, we need to use the Z-score formula:
Z = (X - μ) / σ
Where:
- Z is the Z-score,
- X is the value in the dataset,
- μ is the mean, and
- σ is the standard deviation.
From the Z-distribution table, we know that the Z-score for the 10th percentile is -1.28.
We can plug the values into the Z-score formula and solve for X:
-1.28 = (X - 170) / 10
Multiply both sides by 10:
-12.8 = X - 170
Add 170 to both sides:
X = 157.2
So, the 10th percentile of people's heights is approximately 157.2 cm.
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