Compute Probabilities of a Sample Proportion
-Smith is a weld inspector at a shipyard. He knows from keeping track of good and substandard welds that for the afternoon shift $5 \%$ of all welds done will be substandard. If Smith checks 300 of the 7500 welds completed that shift, what is the probability that he will find between 10 and 20 substandard welds?
A) $0.8132$
B) $0.4066$
C) $0.2033$
D) $0.6377$

Question

Quizplus · Accepted Answer

This problem can be solved using the binomial distribution or approximated with a normal distribution because the sample size is large. The mean ($\mu$) of substandard welds in 300 checks is $300 \times 0.05 = 15$, and the standard deviation ($\sigma$) is $\sqrt{300 \times 0.05 \times 0.95} \approx 5.477$. Converting the problem to a normal distribution, we find the Z-scores for 10 and 20 substandard welds and use the standard normal distribution to find the probabilities. The probability of finding between 10 and 20 substandard welds is approximately 0.8132, making choice A correct.

Compute Probabilities of a Sample Proportion -Smith Is a Weld 5%5 \%5%

Compute Probabilities of a Sample Proportion
-Smith Is a Weld $5 \%$