If we have a normally distributed sample of ages ranging from 1 to 99 years, and we draw a score at random from this distribution, which of the following scores would we be most likely to draw?
A - 9
B - 22
C - 47
D - 86

C - 47

Step-by-step explanation:

In a normal distribution, the values are clustered around the center of curve. The center of the curve is the mean value of the distribution. As we go side ways the number of values decrease with respect to the mean.

A normal distribution is symmetric, the left and right hand side about the mean looks identical.

It is given in the problem that sample of ages follow normal distribution and the range is 1 to 99 years. The mean would most likely to be somewhere close to 50. Now lets assume that the mean of the distribution is indeed 50. Then it means that the number of people having age 50 would be greater than other ages. The number of people having ages 1 or 99 would be least. The closest number to 50 is 47 therefore, 47 is most likely to be drawn if we randomly draw one sample.  

- 2 + 10x³ - 21x² + 19x - 4

step-by-step explanation:

each term in the second factor is multiplied by each term in the first factor

x²(- 2x² + 4x - 1) - 3x(- 2x² + 4x - 1) + 4(- 2x² + 4x - 1) ← distribute

= - 2 + 4x³ - x² + 6x³ - 12x² + 3x -8x² + 16x - 4

collect like terms

= - 2 + 10x³ - 21x² + 19x - 4 ← in standard form

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step-by-step explanation:

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