Market research has indicated that customers are likely tobypass Roma tomatoes that weigh less than

70 grams. A produce company produces Roma tomatoes that average78.0 grams with a standard

deviation of 5.2 grams.

i) Assuming that the normal distribution is a reasonable modelfor the weights of these

tomatoes, what proportion of Roma tomatoes are currentlyundersize (less than 70g)?

ii) How much must a Roma tomato weigh to be among the heaviest20%?

iii) The aim of the current research is to reduce the proportionof undersized tomatoes

to no more than 2%. One way of reducing this proportion is toreduce the standard deviation.

If the average size of the tomatoes remains 78.0 grams, whatmust the target standard deviation

be to achieve the 2% goal?

iv) The company claims that the goal of 2% undersized tomatoesis reached. To test this,

a random sample of 20 tomatoes is taken. What is thedistribution of the number of undersized

tomatoes in this sample if the company's claim is true? Explainyour reasoning.

v) Suppose there were 3 undersized tomatoes in the random sampleof 20. What is the

probability of getting at least 3 undersized tomatoes in arandom sample of 20 if the company's

claim is true? Do you believe the company's claim? Why or whynot?