Question

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 less than 20 substandard welds?

0.9066

0.0934

0.4066

0.5934

Answer 1

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.

Smith checks 300 of the 7500 welds completed that shift.

Now, if X denote the number of substandard welds out of these 300, then X follows binomial with parameters n=300 and p=0.05.

Now, in this proble, n is too large to practically use the binomial distribution.

Also, n*p=300*0.05=15 is also large; so we cannot use the poisson approximation to binomial distribution.

This implies, the best option would be to apply the normal approximation to binomial distribution.

The mean of X is

So, we can say that

X approximately follows normal with mean 15 and standard deviation of 3.7749.

Now, we have to find

Where, Z is the standard normal variate.

Where, phi is the distribution function of the standard normal variate.

From the standard normal table, this becomes

The correct answer is option (A) 0.9066.