n=236

p= 1/365 (probability of person being born on July 4)

Mean = np = (236)(1/365) = 0.64657

Standard deviation = sqrt( np(1-p) ) = sqrt( (236)(1/365) (1-1/365) ) =0.803

Assuming the birthdays are independent and equally probable, you have a binomial distribution.

n = 236

p = 1/365

μ = pn ≈ 0.647

σ² = np(1 - p) ≈ 0.645

σ ≈ 0.803