QUESTIONS:
2013; 2aii
2012; 2diii
expected number
Expectant number (event)= n x Probability(event)
(where n is the sample size or number of trials in the experiment)
The expected number gives the theoretical number of times an event is
expected to occur within a sample size
n or after n trials of an experiment
for instance
EVENT: set of outcomes of intrest.
The expected number is only a theoretical measurement as it is based of data gathered from a sample of
a popoualtion or a number of trials of an experiment
which may not accurately represent the actual population of the event.
When calculating the expected number, you may first
need to calculate the probability of an event occuring,
which can be done based on the data you have been
given from a sample or trials of an experiment.
78% of customers at a supermarket spend more than $20
per visit. In one morning, 236 customers shopped at the
supermarket. How many of these customers would be
expected to spend less than $20?
15% of passengers on an airline travel for buisness reasons.
A randomly selected group of passengers is surveyed and it
is found that 9 of them are buisness travellers. What would
you expect to be the size of the survey group?
When calculating the expected number of an
event, it is important to consider the context
of the question. For example, if the expected
number of people for an event was calculated
to be 14.3, the expected number should be
rounded down to the nearest full number (14)
as you can not get 0.3 of a person.
This equation can also be used to find the probability of an event occuring, given the sample
size and expected number, by working backwards.
practice Question
Solve
78% of customers at a supermarket spend more than $20 per visit. In one morning, 236 customers
shopped at the supermarket. How many of these customers would be expected to spend less than $20?
15% of passengers on an airline travel for buisness reasons. A randomly selected group of passengers
is surveyed and it is found that 9 of them are buisness travellers. What would you expect to be the size
of the survey group?
Example One
Calculate the expected number
Define events and
probabilities
Calculate expected number
Event: customers spend more than $20
Event’: customers spend less than $20
Example Two
Estimate the size of the sample
group
Define events and
probabilities
Event: passengers travel for buisness reasons
Event: passengers don’t travel for buisness reasons
P(customers spend more than $20)= 78% or 0.78
P(passengers travel for buisness reasons)= 15% or 0.15
P(customers spend less than $20)= 1- 0.78
= 0.22
Expected number of passengers who travel for
buisness reasons = 9
P(customers spend less than $20)= 0.22
n (number of customers)= 236
Expected number of customers who spend less
than $20 = n.p
= 236 . 0.22
= 51.92
= 51 customers
And get
Estimate sample
size
Expected number of customers who travel for buisness reasons (E) = n.p
=9
n (number of randomly selected passengers
surveyed) = E
p
= 9
0.15
= 60
51 customers
studytime.co.nz
facebook.com/studytimenewzealand
And get
60 passengers