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viva [34]
3 years ago
5

Approximately 80,000 marriages took place in the state of New York last year. Estimate the probabilitythat for at least one of t

hese couples,(a) both partners were born on April 30;(b) both partners celebrated their birthday on the same day of the year.State your assumptions.
Mathematics
1 answer:
lilavasa [31]3 years ago
7 0

Answer:

a. 0.45 b. 1

Step-by-step explanation:

We will be using Poisson Approximation of Binomial because n = 80,000 is large and probability (<em>p) </em>is very small.

We calculate for (a) as follows:

The probability that both partners were born on April 30 is

<em>p </em>= 1/365 X 1/365

<em>p </em>= 1/133,225

<em>p </em>= 0.00000751

Using Poisson Approximation, we have:

λ = n<em>p</em>

λ = 80,000 X 0.00000751

λ = 0.6

We use λ to calculate thus:

P (X \geq 1) = 1 - P ( X = 0)

              = 1 - e^-λ

              = 1 - e^-0.6

              = 0.451

There is a 45.1% probability that, for at least one of these couples, both partners were born on April 30.

(b) To calculate the probability that both partners celebrated their birthday on the same day:

<em>p </em>(same birthday) = 365 X 1/365 X 1/365

                             = 1/365

λ = n<em>p</em>

λ = 80,000 X 1/365

λ = 219.17

P (X \geq 1) = 1 - P ( X = 0)

= 1 - e^-λ

= 1 - e^-219.17

≈ 1

There is almost 100% probability that, for at least one of these couples, both partners celebrate their birthday on the same day of the year.

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Florence works in the shipping department of a toy factory that makes radio-controlled helicopters. Small helicopters weigh 3 ki
Damm [24]

Answer:

50 kg

Step-by-step explanation:

Given that:

SMALL HELICOPTERS:

Weight of small helicopters = 3kg

Weight of shipping container = 20kg

LARGE HELICOPTERS:

Weight of large helicopters = 4kg

Weight of shipping container = 10kg

Number of helicopters each shipping container can hold = s ; all of the packed containers will have the same shipping weight

Shipping weight :

(Weight per helicopter * number of helicopter) + weight of shipping container

Shipping weight of Small helicopters :

(3kg * s) + 20

Shipping weight Large helicopters :

(4kg * S) + 10

Shipping weight of Small helicopters = shipping weight of large helicopters

3s + 20 = 4s + 10

20 - 10 = 4s - 3s

10 = s

Hence, member of shipped helicopters = 10

Total shipping weight :

(4 * S) + 10

(4*10) + 10

40 + 10 = 50kg

4 0
3 years ago
14 lessons costs $210. What would 72 lessons cost
Oksi-84 [34.3K]

Answer:

$1,080

Step-by-step explanation:

To solve, we can make a proportion

14 lessons are $210 and 72 lessons are $x

14/210=72/x

Cross multiply

14*x=210*72

14x=15120

To solve for x, we need to get x by itself. Since x is being multiplied by 14, divide both sides by 14.

14x/14=15120/14

x=1080

So, 72 lessons will cost $1,080

4 0
3 years ago
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A side of the triangle below has been extended to form an exterior angle of 132°. Find the value of X
Zinaida [17]

Answer:

x = 114°

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles, thus

x + 18° = 132° ( subtract 18° from both sides )

x = 114°

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A triangular prism has a base area or 20 square feet and a height of 4 feet find the volume
ipn [44]

Answer:

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3 years ago
Find the equation of the line with slope m=1 that contains the point (7,5).
katovenus [111]

Answer:

y = x - 2

Step-by-step explanation:

y = mx + b

5 = 1 (7) + b

5 = 7 + b

b = -2

So...

y = x - 2

7 0
2 years ago
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