Agricultural scientists are working on developing an improved variety of Roma to

Question

Agricultural scientists are working on developing an improved variety of Roma tomatoes. Marketing research indicates that customers are likely to bypass Romas that weight less than 70 grams. The current variety of Roma plant produces fruit that average 74 grams, but 11% of the tomatoes are too small. It is reasonable to assume that a Normal model applies.

a) What is the standard deviation of the weights of Romas now being grown?

b) 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 means should they have as a goal?

c) The researchers produce a new variety with a mean weight of 75 grams, which meets the 4% goal. What is the standard deviation of the weights of these new Romas?

d) Based on their standard deviations, compare the tomatoes produced by the two varieties.

Explanation / Answer

I do not have the table or calculator now but I can show you how to solve it, then you can find the exact answer from calculator. 1. First 11% of the tomato is under 70 and the mean is 74. hence, i find the z value that corresponding to .11. then use find the standard derivation by use the fomula: z=(x-mean)/standard derivation where x is 70, mean is 74, and z is what you find in the table or use calculator. 2. find the z value that corresponding to .04. then use find the mean by use the fomula: z=(x-mean)/standard derivation where x is 70, standard derivation is what you find in part a, and z is what you find in the table or use calculator. 3. this is same as part a except mean is 75. 4. the smaller stardard derivation means less variety and consistent of size

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.