1) The outcomes for rolling two dice, the sample space, is as follows:
(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)
There are 36 outcomes in the sample space.
2) The ways to roll an odd sum when rolling two dice are:
(1, 2), (1, 4), (1, 6), (2, 1), (2, 3), (2, 5), (3, 2), (3, 4), (3, 6), (4, 1), (4, 3), (4, 5), (5, 2), (5, 4), (5, 6), (6, 1), (6, 3), (6, 5). There are 18 outcomes in this event.
3) The probability of rolling an odd sum is 18/36 = 1/2 = 0.5
The <em>expected number of mortgages</em> approved per week and the standard deviation of the distribution are 2.019 and 0.024 respectively.
<u>The expected number of mortgages approved per week</u> :
- <em>Mean = (Σfx ÷ Σf)</em>
Expected Number approved = 210 ÷ 104 = 2.019
Hence, it is expected that 2.019 mortageahes would be approved per week.
<u>The standard deviation</u> :
- <em>Variance = [Σ(Xi - x)² ÷ Σf] </em>
- <em>Standard deviation = √Variance</em>
Variance = (59.5414 ÷ 104) = 0.0005698
Standard deviation = √0.0005698
Standard deviation = 0.024
Therefore, the expected value and standard deviation are 2.019 and 0.024 respectively.
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