Starter:

After selling Lotto tickets for 5 years, an agent knows that weekly sales are normally distributed with a mean of $3500 and a standard deviation of $650. What level of weekly sales would the agent exceed 85% of the time?

A salesman travels between Whanganui and Wellington daily. His time for the journey is normally distributed with a mean of 2 hours and 45 minutes (165 minutes) and a standard deviation of 8.0 minutes. What percentage of his trips take:

a) Longer than 3 hoursb) Less than 2 hours and 43 minutesc) Between 2 hours 30 minutes and 2 hours 40 minutes

P(X > 180) = 0.0304 = 3%

P(X < 163 ) = 0.40129 = 40%

P(150 < X < 160 ) = 0.2356 = 23.6%

$2826

Note 12: RISK

When an event is viewed in a negative way then its probability of occurring maybe referred to as a risk

Relative Risk• Used to compare the risk (probability) of an event for

one group with the risk (probability) of an event for another

• The risk for the second group may be referred to as the base-line risk.

• Relative risk = probability of variable present probability of variable not being present

Example:Students were asked to tick a box indicating whether the time they had spent preparing for an assessment was less than 3hr or at least 3hrs – the results are:

1. Calculate the risk of not achieving

2. Calculate the risk for not achieving for students with less than 3hrs preparation

3. The risk for not achieving with at least 3 hours preparation

< 3hrs > 3hrs Total

Achieved 89 145 234

Not Achieved 28 32 60

Total 117 177 294

60/294

28/117

32/177

Example:Students were asked to tick a box indicating whether the time they had spent preparing for an assessment was less than 3hr or at least 3hrs – the results are:

4. Calculate the Relative Risk for not achieving students with less than 3hrs prep compared to not achieved for students that prepared for more than 3hrs

< 3hrs > 3hrs Total

Achieved 89 145 234

Not Achieved 28 32 60

Total 117 177 294

28/117

32/177

= 1.32

A student who studied for <3 hours is 1.32 more likely to fail the assessment than a student who studied for > 3 hours

Workbook Page 171Exercise C