OURCES Chapter 06, Section 6.5, Problem 052 stisn 42 stien Johnson Electronics m

Question

OURCES Chapter 06, Section 6.5, Problem 052 stisn 42 stien Johnson Electronics makes calculators. Consumer satisfaction is one of the top priorities of the company's management. The company quarantees the refund of money or replacement for any calculator that malfunctions within two years from the date of purchase. It is known from past data that despite all efforts, 5% of the calculators manufactured by company malftunction within a 2-year period. The company recently mailed 500 such calculators to iks customers. Find the probability that 14 to 23 of the s00 calculators wll be returned for refund or replacement within a 2-year period. cion Round your answer to four decimal places. estion the absolute tolerance is +/-0.007 etbans. Click if you would like to show Work for this question: 0Shoe Wark Question Attempts: 1 of 5 used SAVE FOR LATER SURIT ANSWER MpleNet Type here to search

Explanation / Answer

Please note nCx = n! / [(n-x)!*x!]

Binomial Probability = nCx * (p)x * (q)n-x, where n = number of trials and x is the number of successes.

Here x = 500, p = 0.05 and q = 0.95

P(14 to 23) = P(14) + P(15) + P(16) + ..... + P(23) = P(0 to 23) - P(0 to 13)

This Can be written as P(At most 23) - P(At most 13)

P( At most 23) using excel Formula BINOMDIST(23,500,0.05,TRUE) = 0.3844

P(At Most 13) using excel Formula BINOMDIST(13,500,0.05,TRUE) = 0.0055

Therefore the required probability = 0.3844

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