Respuesta :
Answer:
About twenty-one percent of twelve month old boys are shorter than 28.8 inches.
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
[tex]\mu = 29.8, \sigma = 1.2[/tex]
About twenty-one percent of twelve month old boys are shorter than what height?
This is the value of X when Z has a pvalue of 0.21. So it is X when Z = -0.805.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.805 = \frac{X - 29.8}{1.2}[/tex]
[tex]X - 29.8 = -0.805*1.2[/tex]
[tex]X = 28.8[/tex]
About twenty-one percent of twelve month old boys are shorter than 28.8 inches.
