Math AI SL Paper 2 May 21 Solution - Question4 #diplomamaths #math #sl

DP Math Applications and Interpretations SL Paper2 May 21
Question 4

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Question 4:

The stopping distances for bicycles travelling at 20 km h -1 are assumed to follow a normal distribution with mean 6.76 m and standard deviation 0.12 m.

(a) Under this assumption, find, correct to four decimal places, the probability that a bicycle chosen at random travelling at 20 km h -1 manages to stop
(I) in less than 6.5 m.
(ii) in more than 7 m.

1000 randomly selected bicycles are tested and their stopping distances when travelling at 20 km h -1 are measured.
(b) Find, correct to four significant figures, the expected number of bicycles tested that stop between
(i) 6.5 m and 6.75 m.
(ii) 6.75 m and 7 m.

The measured stopping distances of the 1000 bicycles are given in the table.
Measured stopping distance | Number of bicycles
Less than 6.5 m | 12
Between 6.5 m and 6.75 m | 428
Between 6.75 m and 7 m | 527
More than 7 m | 33

It is decided to perform a χ 2 goodness of fit test at the 5 % level of significance to decide whether the stopping distances of bicycles travelling at 20 km h -1 can be modelled by a normal distribution with mean 6.76 m and standard deviation 0.12 m.
(c) State the null and alternative hypotheses.
(d) Find the p-value for the test.
(e) State the conclusion of the test. Give a reason for your answer.

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[chemqueef]

THIS is amazing) thank you, I wish my maths teacher explained so well I understand the applications of what I’ve learnt so much better!!