Southwestern Electronics has developed a new calculator that performs a series of functions not yet performed by any other calculator. The marketing department is planning to demonstrate

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Southwestern Electronics has developed a new calculator that performs a series of functions not yet performed by any other calculator. The marketing department is planning to demonstrate this calculator to a group of potential customers, but it is worried about some initial problems, which have resulted in 4 percent of the new calculators developing mathematical inconsistencies. The marketing VP is planning on randomly selecting a group of calculators for this demonstration and is worried about the chances of selecting a calculator that could start malfunctioning. He believes that whether or not a calculator malfunctions is a Bernoulli process, and he is convinced that the probability of a malfunction is really about 0.04. Assuming that the VP selects exactly 50 calculators to use in the demonstration, and using the Poisson distribution as an approximation of the binomial what is the chance of getting no calculators malfunctioning?

Expert Solution
Step 1

From the available information,

The probability of malfunction of calculator is, p=0.04

Number of calculators, n=50

Use the poisson distribution as an approximation to binomial distribution.

Here, the parameter  of poisson distribution Probability homework question answer, step 1, image 1is equal to np.

That is,

Probability homework question answer, step 1, image 2

The probability mass function of poisson distribution is,

Probability homework question answer, step 1, image 3

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