An aerospace engineering student performs an experiment in a wind tunnel to dete

Question

An aerospace engineering student performs an experiment in a wind tunnel to determine the lift coefficient of an airfoil. The student takes 61 measurements of the vertical force using a force balance, yielding a sample mean value of 44.20 N and a sample variance of 4.00 N^2. Determine (a) the percent probability that an additional measurement will be between 45.56 N and 48.20 N, (b) the range (in N) over which the true mean value will be, assuming 90 % confidence, and (c) the range (in N^2) over which the true variance will be assuming 90 % confidence.

Explanation / Answer

Excel formula:

Mean 44.2 Variance 4 Std deviation 2 sample size 61 >30 Assumption: the samples follow Normal distribution (a) P(X<45.56) 75.17% P(X<48.2) 97.72% So, the probability that an additional measurement will be between 45.56 & 48.2 N: P(45.56<X<48.2)= 22.56% (b) Need to compute 90% confidence interval for mean Lower bound 43.7788 N Upper bound 44.6212 N Range= upper-lower 0.841 N (c) Need to compute 90% confidence interval for variance Use Chi-sq distribution to find the CI for variance Lower bound 3.034827 N^2 Upper bound 5.557105 N^2 Range= upper-lower 2.522278 N^2

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