Answers a) 500.98 b) 0.7939 c) 0.8542 Help with solutions!!! Spring exam 2015 Th

Question

Answers

a) 500.98

b) 0.7939

c) 0.8542

Help with solutions!!!

Spring exam 2015 The weights of half liter containers for a soft drink follow a normal distribution with mean 514 g and standard deviation 6 g. If the weight of a half liter container for the soft drink is too small it does not go into retail sale. A certain weight is used as an index that results in 98.5% of the half liter containers going into retail sale, while the remaining 1.5% do not go into retail sale. a) How much does a half liter soft drink container have to weigh to go into retail sale? b) What is the probability that out of 10000 half liter soft drink containers 9860 or less go into retail sale. (Use an approximation). c) What is the probability of a half liter soft drink container weighing more than 508 g given that it goes into retail sale?

Explanation / Answer

a) here for 1.5 percentile ; z=-2.17

hence minimum weight to be quailfied =mean+z*std deviation =514-2.17*6=500.98

b)average number of container go into retail sale =np=0.985*10000=9850

std deviation =(np(1-p))1/2 =12.155

hence P(X<=9860)=P(Z<(9860-9850)/12.155)=P(Z<0.8227)=0.7947

c)P(X>508|X>500.98)=P(Z>1)/0.985=(1-0.1587)/0.985=0.8542

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