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Dafna1 [17]
2 years ago
7

In the United States, 40% of the population have brown eyes (based on data from Dr. P. Sorita Soni at Indiana University). If 14

people are randomly selected, find the probability that at least 12of them have brown eyes.
Mathematics
1 answer:
Sav [38]2 years ago
4 0

Answer:

0.0006087 (4 sf)

Step-by-step explanation:

Binomial distribution:  X ~ B(n, p)

where n is the number of trials and p is the probability of success

Let the random variable X be the number of people with brown eyes

n = 14

p = 40% = 0.4

Therefore,  X ~ B(14, 0.4)

P(X ≥ 12) = 1 - P(X ≤ 11)

              = 1 - 0.9993913226...

              = 0.000608677...

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To solve this first find the area of each of the white shapes inside the rectangle

The formula for the area of a circle is:

A = πr²

In this case we know that the radius is 2

Plug what you know into the area of a circle formula:

A = π2²

A = π4

A = 4π

A ≈ 12.57

The formula for the area of a square is:

A = Length x Height

In this case we know that both length and height are 3

Plug what you know into the formula for area of a square:

A = 3 x 3

A = 9

To find the area of the UNSHADED region simply add together the area of the circle (12.57) with the area of the square (9):

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To find the area of the SHADED region find the total area of the surrounding rectangle then subtract the area of unshaded area from the total area of the surrounding rectangle.

The formula for the area of a rectangle is:

A = Length x Height

The length is 10 and the height is 7

A = 10 x 7

A = 70

Shaded region:

70 - 21.57 = 48.43

Unshaded region: 21.57

Total area of surrounding rectangle: 70

Shaded region: 48.43

Hope this helped!

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