probability marble question

Question

You are given an urn with 40 red marbles and 60 black marbles. You sample a single marble from the urn 25 times with replacement. What is the probability of drawing 13 or more black marbles?

Answer 1

np = mean or expected value = 60% x 25 = 15 black marbles

variance = npq = 15(40%) = 6 black marbles

standard deviation = sqr6

(15-13) = 2

2/sqr6 = z score = 2/sqr2(sqr3) = sqr2/sqr3 = 1.414/1.732 approximately 0.8164

find the corresponding probability from z tables

Should be about 1-0.206 = 0.794 or 79.4% probability of 13 or more black marbles