B only. Step by step please 6.52 Johnson Electronics makes calculators. Consumer

Question

B only. Step by step please

6.52 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 pu- 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. a. Find the probability that exactly 29 of the 500 calculators will be returned for refund or replacement within a 2-year period. b. What is the probability that 27 or more of the 500 calculators will be retuned for refund or replacement within a 2-year period?

Explanation / Answer

b) here from binomial distribution ; mean number of calculators to be returned =np=500*0.05 =25

and std deviation =(np(1-p))1/2 =4.873

as np>10 and n(1-p)>10 we can apply normal distribution:

threfore from normal approximation of binomial distribution:

probability of 27 or more calculators to be returned:

( please revert for any clarification required)

for normal distribution z score =(X-)/ here mean=       = 25 std deviation   == 4.873

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