Edexcel A-Level Mathematics A2 S2.3.2 Normal Approximation to the Binomial Distribution Questions

Practise normal approximations to binomial and Poisson models, including continuity correction and standardised probabilities.

Exam points

write the approximating normal model with mean and variance from binomial or Poisson data
use standardised probability equations to solve for n, p, μ, σ or an unknown length

[Maximum number: 5]

The manager of a supermarket is investigating the number of complaints per day received from customers.

A random sample of 180 days is taken and the results are shown in the table below.

Table for Question Edexcel A-Level Mathematics A2 S2.3.2 Normal Approximation to the Binomial Distribution Questions question 1 — Edexcel A-Level Mathematics A2

A week consists of 7 consecutive days.

Using the manager's model and a suitable approximation, show that the probability that there are less than 19 complaints in a randomly selected week is 0.29 to 2 decimal places.
Show your working clearly.
(Solutions relying on calculator technology are not acceptable.)

for writing or using N(21,21). May be seen in a standardisation expression.
for standardisation $( \pm)$ using their mean and sd. Allow 17.5, 18, 18.5, 19, 19.5, 22.5, 23, 23.5, 24,
24.5
for using $19 \pm 0.5$ or $23 \pm 0.5$
for a fully correct standardisation expression Implied by awrt $\pm 0.546$

A1*

awrt 0.291 or 0.293 from correct working seen

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Edexcel A-Level Mathematics A2 S2.3.2 Normal Approximation to the Binomial Distribution Questions question 1