a) The proportion of broken pencils produced by a factory is 0.0003. The factory produces 10,000 pencils in a batch. Assume that pencils break independently of one another. i) Use a suitable approximation to find the probability that a batch will have at most 1 broken pencil. Numerical evaluation of the answer is required. ii) A store orders 8 batches from the factory. Find the probability that at least two batches have at most 1 broken pencil. Numerical evaluation of the answer is required.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 31E
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Question 5
a) The proportion of broken pencils produced by a factory is 0.0003. The factory
produces 10,000 pencils in a batch. Assume that pencils break independently of one
another.
i) Use a suitable approximation to find the probability that a batch will have at
most 1 broken pencil. Numerical evaluation of the answer is required.
ii) A store orders 8 batches from the factory. Find the probability that at least two
batches have at most 1 broken pencil. Numerical evaluation of the answer is
required.
iii) Another store orders one batch from the factory every week. What is the
expected number of weeks until the store receives a batch with at most 1 broken
pencil. Numerical evaluation of the answer is required.
b) In a group of 76 patients, 8 are diabetic. Twelve patients are selected randomly.
i) Find the probability that no diabetic patients are selected.
ii) the probability that at least two diabetic patients are selected.
Transcribed Image Text:Question 5 a) The proportion of broken pencils produced by a factory is 0.0003. The factory produces 10,000 pencils in a batch. Assume that pencils break independently of one another. i) Use a suitable approximation to find the probability that a batch will have at most 1 broken pencil. Numerical evaluation of the answer is required. ii) A store orders 8 batches from the factory. Find the probability that at least two batches have at most 1 broken pencil. Numerical evaluation of the answer is required. iii) Another store orders one batch from the factory every week. What is the expected number of weeks until the store receives a batch with at most 1 broken pencil. Numerical evaluation of the answer is required. b) In a group of 76 patients, 8 are diabetic. Twelve patients are selected randomly. i) Find the probability that no diabetic patients are selected. ii) the probability that at least two diabetic patients are selected.
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