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

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter8: Sequences, Series,and Probability

Section8.7: Probability

Problem 11ECP: A manufacturer has determined that a machine averages one faulty unit for every 500 it produces....

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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

Expert Solution

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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