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 hot dogs eaten by contestants last year was normally distributed with a mean of 40 and a standard deviation of 5.

Alan Alda fell into the 33rd percentile of hot dog eating. How many hot dogs did he eat (and hot dogs are a continuous variable)?

Answer 1

x = number of hot dogs eaten

for standard normal distribution z = (x - mean)/standard deviation

z-score corresponding to 33% percentile (cumulative probability of 0.33) = -0.44

using above equation and given data:

-0.44 = (x - 40)/5 ---> x = 37.8 hot dogs