Another precise statistic!

 I have been quiet on this blog for a while, not that I have gone away, but there have been so many other matters to deal with.  Hopefully I can get back to the coalface soon.  But today I was startled by this amazing statistic:

This company (a house agent) was so proud of their popularity that they could claim four-figure accuracy about their clients' delight.  As usual, stop and think.  The claim is that 98.96%, not 98.95%, nor 98.97% of clients were satisfied.  As I closed my eyes in the dentist's chair (the glossy brochure had been in the waiting room), I thought about the sample size to give such raw data, and obviously one sample would be of 1250 clients of whom 1237 were pleased.  Of course that would imply that the standard deviation would be quite large as well, and exactly 1250 clients being sampled seemed suspicious.  So, back home I ran through other sample sizes, and, lo and behold, 476 out of a sample of 481 also gives the same percentage to four significant figures.  

I don't know which is most impressive: the statistic, the ignorance of the company doing the survey for the client, or the folly of  the copywriter for the house agent.  What do you think?