The content of Vitamin C ina1 litre carton of blueberry juice is known to have a mean of 36.75 milligrams and a standard deviation of 2.5 milligrams. Assuming the content is normally distributed;

1. Determine the probability that, for a carton chosen randomly, the content of vitamin C is more than 34 milligrams.

Drawa well-labelled diagram with the relevant area shaded.

Show allworking or marks will be deducted

1. What will be thevalue for thelowest 25% of maximum vitamin C content in the blueberry juice?

(Hint: this is equivalent to finding the value of the25thpercentile).

Showall working or marks will be deducted.

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1. Would your answers to parts (a)and (b) changeif the assumption that thevitamin C contentfollowsa normal distributionwasincorrect?

Explainyour answer.

Question 2 [(4 + 2)+3= 9 marks]

The time taken by an Airbus flight from Sydney to Melbourneis assumed to be normally distributed.To establish the time this particular flight takes, the company recorded the time it took35flightsto flyand calculated a mean of95 minutes. Fromhistoricalrecordsthe time takenwas known to havea standard deviation of8.6minutes.

1. (i).Calculate a 90% confidence interval for the population mean time takenby an Airbus flight from Sydney to Melbourne.

Showall steps in your calculation and answer to two decimal places.

(ii).Provideaninterpretation ofthe confidence interval calculated inpart (i).

1. Later, the analyst discovered that thesample sizewas actually53 instead of 35.Without any calculation, explain how this revisedsample sizewould change the confidence interval obtained inpart (a).

Commentontheaccuracy of this confidence intervalcompared to the one in(a)(i).

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Question3 [9+ 2 = 11marks]

1. According tocolleges learning standards, a student is expected to spend more than 28.5 hours per week studying on their own to score more than 80% in their final grades. According to a recent survey of 40 students who scored 80% or more, it wasfoundthat these students spend an average of 30.25 hours and standard deviation of 4.75 hours on their studies per week.

Test if thecollege expectation is correctat the 5% level of significance.

Use thecritical valuemethod.

1. In the context of this question,define anddescribe what is a TypeIerror.