Question 705066

SCQMEDIUM

An astronomer observes 500 objects and classifies them as either of type A or type B. She finds 148 objects to be of type B. Assuming a binomial distribution, the best estimate of the fraction of type A objects and its associated standard deviation respectively are

(A)

0.704,0.002

(B)

0.70,0.02

(C)

0.704,0.031

(D)

0.72,0.03

Detailed Solution

Total objects N=500N=500. Type B objects 148148, so Type A NA=500−148=352N_A = 500 - 148 = 352. Fraction p=352/500=0.704p = 352/500 = 0.704. Standard deviation for binomial distribution is σ=p(1−p)n=0.704×0.296500≈0.000416≈0.0204\sigma = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.704 \times 0.296}{500}} \approx \sqrt{0.000416} \approx 0.0204. Thus, 0.704 and 0.02.

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