advance engineering mathematics help me solving this problem

advance engineering mathematics

help me solving this problem please

etaal measurements of dimensions for 100 samples oa fe i 4 Anal i egivenhetsofdimensionsfor 100samplesoachoffve independ m eponemus are given hy 098 151 048 0.57 1.35 i Mean Standard t);-aria- 01 10.025-0009 1000g T0018 App the central limit theo em and determine therange forthelength L-A+D CHHE to include approximately 95% of the values.

Solution

We have L = A + B + C + D + E = 0.98 + 1.51 + 0.48 + 0.57 + 1.35 = 4.89

Since A, B, C, D, E are independant components,

Var(A + B + C + D + E) = (Var(A) + Var(B) + Var(C) + Var(D) + Var(E)

= 0.011² + 0.025² + 0.009² + 0.008² + 0.018²

= 0.001215

Thus, S.D. (A + B + C + D + E) = squareroot(0.001215) = 0.034857

Similarly n = 100 + 100 + 100 + 100 + 100 = 500

z value at 95% = 1.96

Standard error = S.D.(A+B+C+D+E)/squareroot(500) = 0.034857 / 22.36067

Margin of error = 1.96 * 0.034857 / 22.36067

Thus, confidence interval:

Upper limit: 4.89 + 1.96 * 0.034857 / 22.36067 = 4.8931

Lower limit: 4.89 - 1.96 * 0.034857 / 22.36067 = 4.8869