Edexcel A-Level - June 2019 - Statistics - Question 5 - Exam Paper Walkthrough

Full walkthrough answer to Question 5 on the Edexcel A-Level Mathematics, Statistics paper, June 2019.
A machine puts liquid into bottles of perfume. The amount of liquid put into each bottle, D ml, follows a normal distribution with mean 25 ml.
Given that 15% of bottles contain less than 24.63 ml
a. find, to 2 decimal places, the value of k such that P(24.63 D k) = 0.45
A random sample of 200 bottles is taken.
b. Using a normal approximation, find the probability that fewer than half of these bottles contain between 24.63 ml and k ml.
The machine is adjusted so that the standard deviation of the liquid put into the bottles is now 0.16 ml.
Following the adjustments, Hannah believes that the mean amount of liquid put into each bottle is less than 25 ml.
She takes a random sample of 20 bottles and finds the mean amount of liquid to be 24.94 ml.
c. Test Hannah's belief at the 5% level of significance.
You should state your hypotheses clearly.
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[JackLord-dg]

sorry I don't understand q5 why u add the two probabilities up so it makes 0.6? I understand the method just not why u do this