A group of 100 people start a Scissor Usage Support Group. The rate at which members enter and leave the group is dependent on whether they are right-handed or left-handed.

You are given the following:

(i) The initial membership is made up of 75% left-handed members (L) and 25% right-handed members [math](\mathrm{R})[/math]

(ii) After the group initially forms, 35 new (L) and 15 new (R) join the group at the start of each subsequent year

(iii) Members leave the group only at the end of each year

(iv) [math]q^{L}=0.25[/math] for all years

(v) [math]q^{R}=0.50[/math] for all years

Calculate the proportion of the Scissor Usage Support Group's expected membership that is left-handed at the start of the group's [math]6^{\text {th }}[/math] year, before any new members join for that year.

• 0.76
• 0.81
• 0.86
• 0.91
• 0.96

For the country of Bienna, you are given:

(i) Bienna publishes mortality rates in biennial form, that is, mortality rates are of the form:

(ii) Deaths are assumed to be uniformly distributed between ages [math]2 x[/math] and [math]2 x+2[/math], for [math]x=0,1,2, \ldots[/math]

(iii) [math]{ }_{2} q_{50}=0.02[/math]

(iv) [math]{ }_{2} q_{52}=0.04[/math]

Calculate the probability that (50) dies during the next 2.5 years.

• 0.02
• 0.03
• 0.04
• 0.05
• 0.06

[math]\mathrm{X}[/math] and [math]\mathrm{Y}[/math] are both age [math]61 . \mathrm{X}[/math] has just purchased a whole life insurance policy. [math]\mathrm{Y}[/math] purchased a whole life insurance policy one year ago.

Both [math]\mathrm{X}[/math] and [math]\mathrm{Y}[/math] are subject to the following 3-year select and ultimate table:

The force of mortality is constant over each year of age.

Calculate the difference in the probability of survival to age 64.5 between [math]\mathrm{X}[/math] and [math]\mathrm{Y}[/math].

• 0.035
• 0.045
• 0.055
• 0.065
• 0.075

A life is subject to the following 3 -year select and ultimate table:

You are also given:

(i) [math]e_{60}=1[/math]

(ii) Deaths are uniformly distributed over each year of age

Calculate [math]\stackrel{\circ}{e}_{[58]+2}[/math].

• 1.5
• 1.6
• 1.7
• 1.8
• 1.9

You are given the following information from a life table:

You are also given:

(i) [math]\quad l_{90}=1000[/math] and [math]l_{93}=825[/math]

(ii) Deaths are uniformly distributed over each year of age.

Calculate the probability that (90) dies between ages 93 and 95.5.

• 0.195
• 0.220
• 0.345
• 0.465
• 0.668

You are given:

i) The following extract from a three-year select and ultimate table:

ii) Mortality follows a uniform distribution of deaths over each year of age

Calculate [math]1000_{\left(0.6 \mid 1.5 q_{[52]+1.7}\right)}[/math].

• 91
• 92
• 93
• 94
• 95