Respuesta :
Answer:
P98 = 16.154in
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 z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Men have hip breadths that are normally distributed with a mean of 14.4 in. and a standard deviation of 1.0 in.
This means that [tex]\mu = 14.4, \sigma = 1[/tex]
Find P98
This is the 98th percentile, that is, X when Z has a pvalue of 0.98, so X when Z = 2.054.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]2.054 = \frac{X - 14.1}{1}[/tex]
[tex]X = 2.054 + 14.1[/tex]
[tex]X = 16.154[/tex]
So
P98 = 16.154in
