1..A machine that is programmed to package 1.20 pounds of cereal is being tested

Question

1..A machine that is programmed to package 1.20 pounds of cereal is being tested for its accuracy. In a random sample of 36 cereal boxes, the sample weight and standard deviation are calculated as 1.22 pounds and 0.06 pound, respectively. Check the Central Limit Theorem (CLT) condition.

2.A retailer is looking to evaluate its customer service. Management has determined that the retailer will have to improve its services if the satisfaction rate is lower than 90% among the customers. A survey of 1,200 randomly selected customers showed that 1,086 were satisfied with their customer service. Check the CLT conditions of the proportion.

Explanation / Answer

a) Yes, Central Limit Theorem (CLT) condition applies here as the Sample Size is greater than 30

b) p = 1086/1200 = 0.905

np = 1200*0.905 = 1086>10

n(1-p) = 1200*(1-0.905) = 114>10

So, Central Limit Theorem (CLT) condition applies here

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