The stopping distances for bicycles travelling at 20 kmh 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 kmh manages to stop - (i) in less than 6.5 m. (ii) in more than 7m. 1000 randomly selected bicycles are tested and their stopping distances when travelling at 20 km h 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 x goodness of fit test at the 5% level of significance to decide whether the stopping distances of bicycles travelling at 20 km h 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.
The stopping distances for bicycles travelling at 20 kmh 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 kmh manages to stop - (i) in less than 6.5 m. (ii) in more than 7m. 1000 randomly selected bicycles are tested and their stopping distances when travelling at 20 km h 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 x goodness of fit test at the 5% level of significance to decide whether the stopping distances of bicycles travelling at 20 km h 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.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:The stopping distances for bicycles travelling at 20 kmh 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 kmh manages to stop
--
(i)
in less than 6.5 m.
(ii)
in more than 7m.
1000 randomly selected bicycles are tested and their stopping distances when travelling
at 20 kmh-
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 x goodness of fit test at the 5% level of significance to decide
whether the stopping distances of bicycles travelling at 20 km h 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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