population Height x  P (x) x∙P(x) x2 x2 ∙ p(x) 54 inches  0.05 2.7 2916 145.8 58 inches 0.05 2.9 3364 168.2 60 inches 0.21 12.6 3600 756 61 inches 0.32 19.52 3721 1190.72 62 inches 0.11 6.82 3844 422.84 63 inches 0.05 3.15 3969 198.45 64 inches 0.05 3.2 4096 204.8 66 inches 0.05 3.3 4356 217.8 67 inches 0.11 7.37 4489 493.79    ∑ p(x)= 1 ∑ x∙P(x)= 61.56   ∑ x2 ∙ p(x) = 3798.4 sampling distribution of the  sample   Values frequency probability 1 62.5  1 1/35 2 62.75 1 1/35 3 63 2 2/35 4 63.25 3 3/35 5 63.5 4 4/35 6 63.75 4 4/35 7 64 5 5/35 8 64.25 4 4/35 9 64.5 4 4/35 10 64.75 3 3/35 11 65 2 2/35 12 65.25 1 1/35 13 65.5 1 1/35 Sum   35 1 activity:  Compute for the mean (??̅) and standard deviation (??̅) of the sampling distribution of the sample means and compare these to the mean and standard deviation of the population.

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.