Respuesta :
Answer:
17.62% probability that his height will be less than 66.7 inches
Step-by-step explanation:
Problems of normally distributed samples can be 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 = 69.3, \sigma = 2.8[/tex]
What is the probability that his height will be less than 66.7 inches?
This is the pvalue of Z when X = 66.7. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{66.7 - 69.3}{2.8}[/tex]
[tex]Z = -0.93[/tex]
[tex]Z = -0.93[/tex] has a pvalue of 0.1762
17.62% probability that his height will be less than 66.7 inches
