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A biologist measured the lengths of hundreds of cuckoo bird eggs. Use the relative frequency distribution below to answer the questions that follow.
Lengths of Cuckoo Bird Eggs
\begin{tabular}{|c|c|}
\hline Length (in millimeters) & Percent of eggs \\
\hline $18.75-19.75$ & 0.8 \\
$19.75-20.75$ & 4.0 \\
$20.75-21.75$ & 17.3 \\
$21.75-22.75$ & 37.9 \\
$22.75-23.75$ & 28.5 \\
$23.75-24.75$ & 10.7 \\
$24.75-25.75$ & 0.8 \\
\hline
\end{tabular}
(a) What percent of the group of eggs was less than $21.75 \mathrm{~mm}$ long?
4.0 $\%$
(b) What is the probability that one of the eggs selected at random was at least $19.75 \mathrm{~mm}$ long but less than $21.75 \mathrm{~mm}$ long?
\[
4.0
\]
Submit Answer

Step 1 ：The question asks for two things. First, it asks for the percent of eggs that are less than 21.75 mm long. To find this, we need to add up the percentages of the eggs that fall into the length categories that are less than 21.75 mm.

Step 2 ：Second, it asks for the probability that a randomly selected egg is at least 19.75 mm long but less than 21.75 mm long. To find this, we need to add up the percentages of the eggs that fall into the length categories that are at least 19.75 mm long but less than 21.75 mm.

Step 3 ：From the given data, the lengths of the eggs are [18.75, 19.75, 20.75, 21.75, 22.75, 23.75, 24.75] and the corresponding percentages are [0.8, 4.0, 17.3, 37.9, 28.5, 10.7, 0.8].

Step 4 ：By adding up the percentages of the eggs that are less than 21.75 mm long, we get 22.1%.

Step 5 ：By adding up the percentages of the eggs that are at least 19.75 mm long but less than 21.75 mm, we get 21.3%.

Step 6 ：Final Answer: (a) The percent of the group of eggs that was less than $21.75 \mathrm{~mm}$ long is \(\boxed{22.1\%}\). (b) The probability that one of the eggs selected at random was at least $19.75 \mathrm{~mm}$ long but less than $21.75 \mathrm{~mm}$ long is \(\boxed{21.3\%}\).