CAIE A-Level Mathematics A2 5.5.1 Normal Distribution Questions
Practise using the normal distribution to estimate probabilities, parameters and expected frequencies.
- Syllabus
- 2028–2030
- Course
- Mathematics 9709
- Level
- A2
Exam points
- use normal distribution models with given mean and standard deviation
- find normal probabilities and parameter values
- interpret normal probabilities and expected frequencies in context
CAIE A-Level Mathematics A2 5.5.1 Normal Distribution Questions question 1
[Maximum number: 4]
The mass of grapes sold per day by a large shop can be modelled by a normal distribution with mean 28 kg . On 10 % of days less than 16 kg of grapes are sold.
In a random sample of 365 days, on how many days would you expect the mass of grapes sold to be within 1.3 standard deviations of the mean?
The probability of being within 1.3 standard deviations of the mean is
P(−1.3<Z<1.3)=2Φ(1.3)−1=2(0.9032)−1=0.8064.
In 365 days, the expected number is
365(0.8064)=294.3,
so the answer is 294 days.
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