The length of a 15-year-old female's upper arm is approximately normally distributed with mean $\mu=35.2 \mathrm{~cm}$ and a standard deviation of $\sigma=2.9 \mathrm{~cm}$. Complete parts (a) through (c) below.
c.
D.
(c) Suppose the area under the normal curve to the left of $x=30 \mathrm{~cm}$ is 0.0365 . Provide two interpretations of this result. Select all that apply.

The proportion of 15 -year-old females with an upper arm length $30 \mathrm{~cm}$ is 0.0365 .

The probability that a randomly selected 15 -year-old female has an upper arm length $30 \mathrm{~cm}$ is 0.0365
(1) Time Remaining: 00:54:03
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Step 1 ：The question is asking for interpretations of the given probability in the context of the problem. The area under the normal curve to the left of a certain value represents the proportion of the population that falls below that value. In this case, the area to the left of 30 cm is 0.0365, which means that 3.65% of the population (15-year-old females) have an upper arm length less than 30 cm. This can be interpreted in two ways:

Step 2 ：The proportion of 15-year-old females with an upper arm length less than 30 cm is 0.0365.

Step 3 ：The probability that a randomly selected 15-year-old female has an upper arm length less than 30 cm is 0.0365.

Step 4 ：Final Answer: The two interpretations of the result are:

Step 5 ：\(\boxed{\text{The proportion of 15-year-old females with an upper arm length less than 30 cm is 0.0365.}}\)

Step 6 ：\(\boxed{\text{The probability that a randomly selected 15-year-old female has an upper arm length less than 30 cm is 0.0365.}}\)