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Ksju [112]
3 years ago
14

A company that sells annuities must base the annual payout on the probability distribution of the length of life of the particip

ants in the plan. Suppose the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 68 years and a standard deviation of 3.5 years (Show your workings clearly).
a) What proportion of the plan recipients would receive payments beyond age 75?

b) What proportion of the plan recipients die before they reach the standard retirement age of 65?

c) Find the age at which payments have ceased for approximately 86% of the plan participants.
Mathematics
1 answer:
Svetlanka [38]3 years ago
5 0

Answer:

Step-by-step explanation:

Let X be length of life of the participants in the plan.

Given that X is N(68,3.5)

We convert this to standard normal score z using

z=\frac{x-68}{3.5}

a)  proportion of the plan recipients that would receive payments beyond age 75=P(X\geq 75) = P(Z\geq 2)\\= 0.025

b) proportion of the plan recipients die before they reach the standard retirement age of 65=P(X\leq 65) = P(z\leq -0.86)\\=0.5-0.2764\\=0.2236

c) x for 86% ceased

P(Z

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Sedbober [7]

Answer:

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Step-by-step explanation:

<u><em>The correct question is</em></u>

The two rectangles show are similar. Find the value of x

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

In this problem

\frac{20}{14}=\frac{x}{6}

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x=\frac{20}{14}(6)

x=\frac{120}{14}\ units

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x=\frac{60}{7}\ units=\frac{56}{7}+\frac{4}{7}=8\frac{4}{7}\ units

4 0
3 years ago
A diver started at 4 feet above ground. After diving he ended at 58 feet below the surface
Andrews [41]

Answer:

62

Step-by-step explanation:

If the diver started 4 four feet above the ground and ended 58 feet below the surface, the diver went down, so we can solve this by taking the total distance traveled like so:

|4+58| = 62

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3 years ago
I dont understand can someone help?
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3 0
2 years ago
In right trapezoid MNPQ
Gala2k [10]

Answer:

  about 252.78 ft

Step-by-step explanation:

Define angle QMP as α. Then ...

  MN = 60·sin(α)

  NP = 60·cos(α)

  area MPN = (1/2)(MN)(NP) = 1800sin(α)cos(α)

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  PQ = 60tan(α)

  area MPQ = (1/2)(MP)(PQ) = 1800tan(α)

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The ratio of areas is 2.5, so we have ...

  1800tan(α) = 2.5·1800sin(α)cos(α)

  1 = 2.5cos(α)² . . . . . . divide by 1800tan(α)

  cos(α) = √0.4 . . . . . . solve for cos(α)

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Then the perimeter is ...

  Perimeter = MN +NP +PQ +QM = 60sin(α) +60cos(α) +60tan(α) +60/cos(α)

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The perimeter of the trapezoid is about 252.776 feet.

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3 0
3 years ago
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dolphi86 [110]

Answer:

The population changed by 20% in 3 years

Step-by-step explanation:

The percentage change, is given by the following equation;

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The initial population of the town = 35,000

The final population of the town = 42,000

The percentage change in the population is therefore;

Percentage \ change \ in \ population= \dfrac{42,000 - 35,000 }{35,000} \times 100 = 20 \%

The population changed (increase) by 20% in 3 years.

3 0
3 years ago
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