I have this set of problems in my homework and I am completely stuck. I just cannot even think of a way to do this.
Obviously the mean is 74. However I cannot think of how to get standard deviation, the only way we have been taught to do that is through taking a set of numbers minus the mean and then dividing my total observations minus 1. I have no idea how to find this target mean, etc.
You don't have to do the problem for me. However I would appreciate it if you could help me figure out how to do them (equation/procedure) etc. I can figure out (C) myself but (A) and (B) I am 100% lost.
5. Growing Tomatoes. 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 than 70 grams. The current variety of Roma plants produces fruit that average 74 grams, but 11% of all tomatoes are too small, i.e. less than 70 grams. It is reasonable to assume that a Normal distribution applies to the weight of all Roma tomatoes.
(a) What is the standard deviation of the weights of Roma tomatoes 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 mean should they have as a goal?
(c) The researchers produced a new variety with a mean of 75 grams and a standard deviation of 2.86g which also meets the 4% goal. Based on their standard deviations, compare the tomatoes produced by the two varieties. Which one would you prefer to grow for selling purposed and why?
Obviously the mean is 74. However I cannot think of how to get standard deviation, the only way we have been taught to do that is through taking a set of numbers minus the mean and then dividing my total observations minus 1. I have no idea how to find this target mean, etc.
You don't have to do the problem for me. However I would appreciate it if you could help me figure out how to do them (equation/procedure) etc. I can figure out (C) myself but (A) and (B) I am 100% lost.
5. Growing Tomatoes. 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 than 70 grams. The current variety of Roma plants produces fruit that average 74 grams, but 11% of all tomatoes are too small, i.e. less than 70 grams. It is reasonable to assume that a Normal distribution applies to the weight of all Roma tomatoes.
(a) What is the standard deviation of the weights of Roma tomatoes 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 mean should they have as a goal?
(c) The researchers produced a new variety with a mean of 75 grams and a standard deviation of 2.86g which also meets the 4% goal. Based on their standard deviations, compare the tomatoes produced by the two varieties. Which one would you prefer to grow for selling purposed and why?