Chapter 06, Section 6.5, Problem 052c Johnson Electronics makes calculators. Con

Question

Chapter 06, Section 6.5, Problem 052c

Johnson Electronics makes calculators. Consumer satisfaction is one of the top priorities of the company's management. The company guarantees the refund of money or a 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 this company malfunction within a 2-year period. The company recently mailed 500 such calculators to its customers. Find the probability that 14 to 23 of the 500 calculators will be returned for refund or replacement within a 2-year period.

Round your answer to four decimal places.

P=

Chapter 06, Section 6.5, Problem 052c

Johnson Electronics makes calculators. Consumer satisfaction is one of the top priorities of the company's management. The company guarantees the refund of money or a 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 this company malfunction within a 2-year period. The company recently mailed 500 such calculators to its customers. Find the probability that 14 to 23 of the 500 calculators will be returned for refund or replacement within a 2-year period.

Round your answer to four decimal places.

P=

Explanation / Answer

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

Here n = 500, p = 0.05, q = 1 – p = 0.95

P( 14 <= X <= 23) = P(At most 23) - P(At most 14) + P(X = 14)

Using software P(At most 23) = 0.3899, P(At most 14) = 0.0108 and P(x = 14) = 0.0053

Therefore the required probability = 0.3899 - 0.0108 + 0.0053 = 0.3844

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