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Answer :
Answer with explanation:
Given : The heights of adult females follow a normal distribution with a mean of 65 inches and a standard deviation of 3.5 inches.
i.e. [tex]\mu=65[/tex] [tex]\sigma=3.5[/tex]
A modeling agency requires female fashion models to be at least 5 feet and 8 inches tall (i.e., 68 inches tall).
Let x denotes the height of adult females.
Formula = [tex]z=\dfrac{x-\mu}{\sigma}[/tex]
Then, the probability of randomly selecting an adult female whose height is greater than the 68 inch requirement for fashion models at this agency :
[tex]P(x>68)=P(\dfrac{x-\mu}{\sigma}>\dfrac{68-65}{3.5})[\\\\\approx P(z>0.86)\ \ [\text{Rounded to two-decimal places.}]\\\\=1-P(z<0.86)\ \ [\because P(Z>z)=1-P(Z The shape of normal curve is bell -shaped. Sketch of the probability distribution is attached below. Hence, the required probability = 0.1949
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