A tire manufacturer has advertised that only 2% of its tires have surface blemishes. Further, the manufacturer argues that tires with such blemishes are perfectly safe, and with only the physical appearance suffering very slightly. A consumer magazine randomly purchases 40 of the tires for an upcoming tire performance comparison report. Upon examining the tires, the magazine’s test engineers find that 5 of them have surface blemishes. If it were true that just 2% of the tires produced have surface blemishes, what would be the probability of getting 5 or more with such blemishes in a random sample of 40 tires? Considering this probability, comment on the believability of the tire manufacturer’s advertising claim.
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