Statistics and probability

Question

Every year "Nathan's hotdog stand of Coney Island NY holds a hot dog eating contest. Assume the that number of hotdogs eaten by contestants last year was normally distributed with a mean of 40 and a standard deviation of 5.

Robert Patterson bet $250,000 from his friend Wesley Snipes that he can be make the top 13%* of hot dog eaters. What is the least number of hot dogs that he needs to eat to win the bet?

*use closest z even if it's lower in this case

Answer 1

use equation for z = (x - mean)/standard deviation, where x here is the number of hot dogs, mean = 40 and standard deviation = 40.

Top 13% of hot dog eaters, places him at the 87th percentile. z corresponding to 87% percentile from table is approximately 1.13.

using above equation with z = 1.13

1.13 = (x - 40)/5 ---> 45.65 hot dogs