Johnson Electronics makes calculators. Consumer satisfac- tion is one of the top

Question

Johnson Electronics makes calculators. Consumer satisfac- tion 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 pur- chase. 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.What is the probability that 27 or more of the 500 calculators will be returned for refund or replacement within a 2-year period?

Explanation / Answer

Ans:

Given that

p=0.05,n=500

Use normal approximation:

mean=500*0.05=25

standard deviation=sqrt(500*0.05*0.95)=4.873

Use continuity correction factor 0.5

P(x>=27)=1-P(x<=26)=1-P(x<=26.5)

z(27.5)=(27.5-25)/4.873=0.3078

P(z>=0.3078)=0.3791

using binomial distrubution:

P(x>=27)=1-BINOMDIST(26,500,0.05,TRUE)=0.3686

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