Respuesta :
Answer:
0.1350 = 13.50% probability that an 18-year-old man selected at random is between 68 and 70 inches tall
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 question, we have that:
[tex]\mu = 69, \sigma = 6[/tex]
What is the probability that an 18-year-old man selected at random is between 68 and 70 inches tall?
This is the pvalue of Z when X = 70 subtracted by the pvalue of Z when X = 68. So
X = 70
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{70 - 69}{6}[/tex]
[tex]Z = 0.17[/tex]
[tex]Z = 0.17[/tex] has a pvalue of 0.5675
X = 68
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{68 - 69}{6}[/tex]
[tex]Z = -0.17[/tex]
[tex]Z = -0.17[/tex] has a pvalue of 0.4325
0.5675 - 0.4325 = 0.1350
0.1350 = 13.50% probability that an 18-year-old man selected at random is between 68 and 70 inches tall
