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Question 3

Discrete random variables

SL 4.1

Medium

[Maximum mark: 6]

A supermarket analyses the shopping habits of its customers.
The number of times, $X$ , each customer visits the supermarket in a week is given by the following probability distribution.

$x$	1	2	3	4	5	$\geq 6$
$\mathrm{P}(X=x)$	$1.5 a$	$2 a$	0.281	$a$	0.026	0

(a)
- (i) Find the value of $a$ .
- (ii) Write down the mode of $X$ . [3]
(b) Find the mean of $X$ . [2]

The manager wants to know why customers come to their supermarket. They survey the first 50 customers to arrive at the supermarket on a particular day.

Simple random / Systematic / Convenience / Quota / Stratified

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