(b) [13 marks] Marina captured a 5-year-old male tuatara on Titi Island weighing

673g (grams). She expects that the weights of 5-year-old male tuatara on Titi

Island will also be normally distributed, and has data suggesting that the mean

and standard deviation on Titi will be respectively = 457g and σ = 108g.

Use the properties of the standard normal random variable Z and Excel to

calculate the following, using these values of u and o. Draw a careful sketch

of the Normal curve for each of parts 3 to 6 (iii. to vi.), shading the area that

corresponds to your answer.

i. Find the standardised score (Z-score) for this individual male. Show your

calculation.

ii. What does your answer to 6(b)i tell us about this tuatara relative to others?

iii. What proportion of tuatara on Titi Island weigh less than the mean?

iv. Find the probability that Marina will encounter a heavier male tuatara on

Titi than the one in 6(b)i

v. Find the probability that the next tuatara Marina measures on Titi will

weigh between 241 grams and 673 grams.

vi. For Titi Island tuatara, find P(| Z |> 3) (see week 4 notes for an example

of this modulus' notation)