Respuesta :
Answer:
The bottom cutoff heights to be eligible for this experiment is 66.1 inches.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions 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.
Mean of 69.0 inches and a standard deviation of 2.8 inches.
This means that [tex]\mu = 69, \sigma = 2.8[/tex]
What is the bottom cutoff heights to be eligible for this experiment?
The bottom 15% are excluded, so the bottom cutoff is the 15th percentile, which is X when Z has a pvalue of 0.15. So X when Z = -1.037.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.037 = \frac{X - 69}{2.8}[/tex]
[tex]X - 69 = -1.037*2.8[/tex]
[tex]X = 66.1[/tex]
The bottom cutoff heights to be eligible for this experiment is 66.1 inches.
