A bag contains on average 170 chocolate covered raisins. Productionstandards req

Question

A bag contains on average 170 chocolate covered raisins. Productionstandards required that in 95% of all bags the number of raisinsdoes not deviate from 170 by more than 10. Assume that the numberof raisins is normally distributed with mean andvariance (sigma squared). ANSWERS: Sigma is supposed to be 6.098and b) is supposed to be 0.4013
a) Determine and sigma. (I got the as170). b) A shipment contains 100 bags. What is the probability thatno bag contains less than 160 raisins?
a) Determine and sigma. (I got the as170). b) A shipment contains 100 bags. What is the probability thatno bag contains less than 160 raisins?

Explanation / Answer

95% corresponds to a z score of 1.96 Therefore, 1.96 = 10/ = 10/1.96 = 5.102 The answer you have (6.098) corresponds to a z-score of 1.64 and iswrong. This would be if 90% of all bags were within 10 of170. the probability of a single bag containing more than 160 is97.5% The probability of all 100 containing more than 160 is(.975)100= 0.0795 .4013 is wrong, would be (.99)100

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