Using the normal distribution, the 75th percentile for a 10 month-old girl is 74 centimeters.
Normal Probability Distribution
The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
- The z-score measures how many standard deviations the measure is above or below the mean.
- Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
The mean and the standard deviation are given, respectively, by:
[tex]\mu = 72, \sigma = 3[/tex]
The 75th percentile is X when Z = 0.675, hence:
0.675 = (X - 72)/3
X - 72 = 3 x 0.675
X = 74.
The 75th percentile for a 10 month-old girl is 74 centimeters.
More can be learned about the normal distribution at https://brainly.com/question/15181104
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