When dragons on planet Pern lay eggs, the eggs are either green or yellow. The biologists haveobserved over the years that 30% of the eggs are yellow, and the rest green. Next spring the leadscientist has permission to randomly select 44 of the dragon eggs to incubate. Consider all thepossible samples of 44 dragon eggs.What is the usual number of yellow eggs in samples of 44 eggs? (Give answers as SENSIBLE wholenumbers.)minimum usual number of yellow eggs =maximum usual number of yellow eggs =

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Description: When dragons on planet Pern lay eggs, the eggs are either green or yellow. The biologists haveobserved over the years that 30% of the eggs are yellow, and the rest green. Next spring the leadscientist has permission to randomly select 44 of the drag

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Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.6: Summarizing Categorical Data

Problem 10CYU

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When dragons on planet Pern lay eggs, the eggs are either green or yellow. The biologists have
observed over the years that 30% of the eggs are yellow, and the rest green. Next spring the lead
scientist has permission to randomly select 44 of the dragon eggs to incubate. Consider all the
possible samples of 44 dragon eggs.
What is the usual number of yellow eggs in samples of 44 eggs? (Give answers as SENSIBLE whole
numbers.)
minimum usual number of yellow eggs =
maximum usual number of yellow eggs =

Expert Solution

Step 1

According to central limit theorem, if sampling distribution of sample proportion with conditions $n p \geq 10$ and $n (1 - p) \geq 10$ , is generated then the sample proportion follows the normal distribution with mean $μ_{\hat{p}} = p$ and standard deviation $σ_{\hat{p}} = \sqrt{\frac{p (1 - p)}{n}}$ .

Here, the sample size is $n = 44$ and population proportion is 30% or $p = 0.30$ . First compute the value of $n p and n (1 - p)$ .

$\begin{array}{rcl} n p & = & 44 \cdot 0.30 \\ = & 13.2 \\ n (1 - p) & = & 44 \cdot (1 - 0.30) \\ = & 44 \cdot 0.70 \\ = & 30.8 \end{array}$

Both the values are more than 10, thus the central limit theorem can be applied.

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