Answered: We are picking 200 jelly beans out of a…

Name: We are picking 200 jelly beans out of a huge vat at a factory known to
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Description: We are picking 200 jelly beans out of a huge vat at a factory known to have 25% black jelly beans. Use the normal approximation to the binomial to find the probability that we get 60 or fewer black jelly beans

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter8: Sequences, Series, And Probability

Section8.7: Probability

Problem 33E: Find the probability of each event. Drawing 5 orange cubes from a bowl containing 5 orange cubes and...

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We are picking 200 jelly beans out of a huge vat at a factory known to have 25% black jelly beans. Use the normal approximation to the binomial to find the probability that we get 60 or fewer black jelly beans

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Step 1

$s a m p l e s i z e (n) = 200$

$p r o b a b i l i t y (p) = 0.25$

Using normal approximation to binomial we have

$\begin{array}{rcl} m e a n (μ) & = & n p \\ = & 200 \times 0.25 \\ = & 50 \end{array}$

$\begin{array}{rcl} s \tan d a r d d e v i a t i o n (σ) & = & \sqrt{n p (1 - p)} \\ = & \sqrt{200 \times 0.25 \times (1 - 0.25)} \\ = & \sqrt{200 \times 0.25 \times 0.75} \\ = & \sqrt{37.5} \\ = & 6.123724 \end{array}$

Using continuity criteria we have

$\begin{array}{rcl} x & = & 60 + 0.5 \\ = & 60.5 \end{array}$

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