Group Questions – Normal Calculations

  1. Hens usually begin laying eggs when they are about 6 months old. Young hens tend to lay smaller eggs, often weighing less than the desired minimum weight of 54 grams.
  2. The average weight of the eggs produced by the young hens is 50.9 grams, and only 28% of their eggs exceed the desired minimum weight. If a Normal model is appropriate, what would the standard deviation of the egg weights be?
  3. By the time these hens have reached the age of 1 year, the eggs they produce average 67.1 grams, and 98% of them are above the minimum weight. What is the standard deviation for the appropriate Normal model for these older hens?
  4. Are egg sizes more consistent for the younger hens or the older ones? Explain.
  5. A certain poultry farmer finds that 8% of his eggs are underweight and that 12% weigh over 70 grams. Estimate the mean and standard deviation of his eggs.
  1. Agricultural scientists are working on developing an improved variety of Roma tomatoes. Marketing research indicates that customers are likely to bypass Romas that weigh less than70 grams. The current variety of Roma plants produces fruit that average 74 grams, but 11% of the tomatoes are too small. It is reasonable to assume that a Normal model applies.
  2. What is the standard deviation of the weights of Romas now being grown?
  3. Scientists hope to reduce the frequency of undersized tomatoes to no more than 4%. One way to accomplish this is to raise the average size of the fruit. If the standard deviation remains the same, what target mean should they have as a goal?
  4. The researches produce a new variety with a mean weight of 75 grams, which just meets the 4% goal. What is the standard deviation of these new Romas?
  5. Based on their standard deviations, compare the tomatoes produced by the two varieties.
  1. A company that markets build-it-yourself furniture sells a computer desk that is advertised with the claim “less than an hour to assemble.” However, through post-purchase surveys the company has learned that only 25% of their customers succeeded in building the desk in under an hour; 5% said it took them over 2 hours. The company assumes that consumer assembly time follows a Normal model.
  2. Find the mean and standard deviation of the assembly time model.
  3. One way the company could solve this problem would be to change the advertising claim. What assembly time should the company quote in order that 60% of customers succeeded in finishing the desk by then?
  4. Wishing to maintain the “less than and hour” claim, the company hopes that revising the instructions and labeling the parts more clearly can improve the 1-hour success rate to 60%. If the standard deviation stays the same, what new lower mean time does the company need to achieve?
  5. Months later, another post-purchase survey shows that new instructions and part labeling did lower the mean assembly time, but only to 50 minutes. Nonetheless, the company did achieve the 60%-in-an-hour goal too. How was that possible?