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Answer:
Jennifer's height is 63.7 inches.
Step-by-step explanation:
Let <em>X</em> = heights of adult women in the United States.
The random variable <em>X</em> is normally distributed with mean, <em>μ</em> = 65 inches and standard deviation <em>σ</em> = 2.4 inches.
To compute the probability of a normal random variable we first need to convert the raw score to a standardized score or <em>z</em>-score.
The standardized score of a raw score <em>X</em> is:
These standardized scores follows a normal distribution with mean 0 and variance 1.
It is provided that Jennifer is taller than 70% of the population of U.S. women.
Let Jennifer's height be denoted by <em>x</em>.
Then according to the information given:
P (X > x) = 0.70
1 - P (X < x) = 0.70
P (X < x) = 0.30
⇒ P (Z < z) = 0.30
The <em>z</em>-score related to the probability above is:
<em>z</em> = -0.5244
*Use a <em>z</em>-table.
Compute the value of <em>x</em> as follows:
Thus, Jennifer's height is 63.7 inches.