Agricultural scientists are working on developing an improved variety of Roma tomatoes. Market

research has indicated that customers are likely to bypass Romas that weigh less than 70 grams. The

current variety produces fruit that average 74.0 grams with a standard deviation of 3.3 grams.

(a)

[2 marks]

Assuming that the normal distribution is a reasonable model for the weights of these

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

(b)

[3 marks]

The aim of the current research is to reduce the proportion of undersized tomatoes

to no more than 4%. One way of reducing this proportion is to raise the average size of the fruit. If

the standard deviation remains the same, what must the target mean be to achieve the 4% goal?

(c)

[3 marks]

Another way of reducing the proportion of undersized tomatoes is to reduce the

standard deviation. If the average size of the fruit remains 74.0 grams, what must the target standard

deviation be to achieve the 4% goal?

(d)

[2 marks]

Assuming that the goal of 4% undersized tomatoes is reached, what is the probability

of getting no more than 1 undersized tomato in a randomly selected sample of 20 tomatoes