All tomatoes that a certain supermarket buys from growers must meet the store’s specifications of a mean diameter of 6.0 cm and a standard deviation of no more than 0.2 cm. The supermarket’s buyer visits a potential new supplier and selects a random sample of 36 tomatoes from the grower’s greenhouse. The diameter of each tomato is measured, and the mean is found to be 5.94 and the standard deviation is 0.24. Do the tomatoes meet the supermarket’s specs?
a. Determine whether an assumption of normality is reasonable. Explain.
b. Is the sample evidence sufficient to conclude that the tomatoes do not meet the specs with regard to the mean diameter? Use a = 0.05
c. Is the sample evidence sufficient to conclude that the tomatoes do not meet the specs with regard to the standard deviation? Use a = 0.05
d. Write a short report for the buyer outlining the findings and recommendations as to whether or not to use this tomato grower to supply tomatoes for sale in the supermarket.