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LUCKY_DIMON [66]
3 years ago
6

Suppose that x is the probability that a randomly selected person is left handed. The value (1-x) is the probability that the pe

rson is not left handed. In a sample of 1000 people, the function V(x)=1000x(1-x) represents the variance of the number of left-handed people in a group of 1000. What is the maximum variance?
Mathematics
1 answer:
harina [27]3 years ago
4 0

Answer:

The maximum variance is 250.

Step-by-step explanation:

Consider the provided function.

V(x)=1000x(1-x)

V(x)=1000x-1000x^2

Differentiate the above function as shown:

V'(x)=1000-2000x

The double derivative of the provided function is:

V''(x)=-2000

To find maximum variance set first derivative equal to 0.

1000-2000x=0

x=\frac{1}{2}

The double derivative of the function at x=\frac{1}{2} is less than 0.

Therefore, x=\frac{1}{2} is a point of maximum.

Thus the maximum variance is:

V(x)=1000(\frac{1}{2})-1000{\frac{1}{2}}^2

V(x)=250

Hence, the maximum variance is 250.

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