6. [28 marks]

(a) [15 marks] Marina knows that the weights of 5-year-old male tuatara on North

Brother Island are normally distributed with mean = 420 grams and standard

deviation o = 98 grams. Using the Normal distribution and Excel, calculate

the following. Provide the Excel functions you use. Draw a careful sketch of

the Normal curve for all parts, each time showing the area that corresponds to

your answer.

i. The proportion of NBI males that are lighter than 457 grams (the suspected

average weight of Titi Island 5-year-old males).

ii. The proportion that weigh more than 400 grams.

iii. The proportion of males that weigh between 400 grams and 500 grams.

iv. The weight at which a male is lighter than 85% of individuals.

v. All males in the top 20% for weight are expected to be sexually mature.

How much does the lightest sexually mature male weigh?