You’ve been hired as a consultant for Spotifly to conduct a survey for them regarding customer satisfaction. From a random selection and poll of 1000 individuals (out of their 718,000 customers), you...

You’ve been hired as a consultant for Spotifly to conduct a survey for them regarding customer satisfaction.

From a random selection and poll of 1000 individuals (out of their 718,000 customers), you found that 63% were HIGHLY SATISFIED with Spotifly’s services.  Surprisingly, the management team of Spotifly is furious with you and, as they are kicking you out of their building, they yell “At Spotifly, our customers  love us!  Everyone knows that two-thirds of our customers are HIGHLY SATISIFIED with us!”

Hmm… is that really the case?  That is, assuming they are right, then how likely is it to observe poll results so far below the true “high satisfaction” rate?  (three decimals)