A-Level MathematicsYear 2021Q5
14 5. The heights of females from a country are normally distributed with • a mean of 166.5 cm • a standard deviation of 6.1 cm Given that 1% of females from this country are shorter than k cm, (a) find the value of k (2) (b) Find the proportion of females from this country with heights between 150 cm and 175 cm (1) A female, from this country, is chosen at random from those with heights between 150 cm and 175 cm (c) Find the probability that her height is more than 160 cm (4) The heights of females from a different country are normally distributed with a standard deviation of 7.4 cm Mia believes that the mean height of females from this country is less than 166.5 cm Mia takes a random sample of 50 females from this country and finds the mean of her sample is 164.6 cm (d) Carry out a suitable test to assess Mia’s belief. You should • state your hypotheses clearly • use a 5% level of significance (4) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________
Paper Source:9MA0_31_que_20211019.pdf
Get full Socratic AI guidance on this question — free in the Applaa desktop app
Appy Buddy guides you step-by-step toward the answer without giving it away. Type your attempt and get instant, mark-scheme-aware clues that teach you to think like an examiner.
Applaa Desktop App
Join Applaa Community
Create your own games, learn AI concepts, program interactive apps, and share with a kid-safe community approved by parents. Free forever on Windows and Mac.
Download Free
Available for Windows and macOS · COPPA Compliant
Exam Specification Info
This question is part of the UK A-Level Mathematics syllabus. In the actual exam, structured questions typically require linking specific keywords to gain full marks. Applaa helps you drill these topics.
Syllabus levelAdvanced Level (A-Level)
SubjectMathematics
Official MarksVariable (2–6 marks)