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.

Steve Buscemi can eat 36 hotdogs. What percentile does he fall in?

(make sure to multiply by 100 and THEN use 2 decimals)

Answer 1

x = number of hot dogs eaten

Determine the probability of eating less 36 hot dogs using standard normal distribution

and z-statistic = (x - mean) / standard deviation

P(x < 36 ) = P(z < (36 -40)/5) = P(z < -0.8) = 0.2119

percentile = 0.2119 * 100 = 21.19%