Скачать или смотреть Edexcel A-Level Mathematics - October 2020 - Statistics - Question 5 - Exam Paper Walkthrough

Full walkthrough answer to Question 5 on the Edexcel A-Level Mathematics, Statistics paper, October 2020.
A health centre claims that the time a doctor spends with a patient can be modelled by a normal distribution with a mean of 10 minutes and a standard deviation of 4 minutes.
(a) Using this model, find the probability that the time spent with a randomly selected patient is more than 15 minutes.
Some patients complain that the mean time the doctor spends with a patient is more than 10 minutes.
The receptionist takes a random sample of 20 patients and finds that the mean time the doctor spends with a patient is 11.5 minutes.
(b) Stating your hypotheses clearly and using a 5% significance level, test whether or not there is evidence to support the patients’ complaint.
The health centre also claims that the time a dentist spends with a patient during a routine appointment, T minutes, can be modelled by the normal distribution where T ~ N(5, 3.52)
(c) Using this model,
(i) find the probability that a routine appointment with the dentist takes less than 2 minutes
(ii) find P (T smaller than 2 | T larger than 0)
(iii) hence explain why this normal distribution may not be a good model for T.
The dentist believes that she cannot complete a routine appointment in less than 2 minutes.
She suggests that the health centre should use a refined model only including values of T larger than 2
(d) Find the median time for a routine appointment using this new model, giving your answer correct to one decimal place.
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