Help with probability!!! Not good at probability!

Question

Help with number 17???
On a fair coin, each side has an equal probability of coming up. When a fair coin is flipped n rimes, the most likely outcome (the mean) is that each side will come up times, with a standard deviation of sigma Megan flips a coin 50 times. She will conclude that the coil is unfair if the number of times cither side is flipped is outside 1.5 standard deviations of the mean. Show your calculations to complete the statement below. The coin will be considered fair if her results show "heads" at least ___ times and no more than __ times. My guess is n=50 and I plug it into the equation: simga=√50/2 =3.535 and then u multiply 3.535 by 1.5(stardand deviation of the mean) and get 5.303. I'm guessing the mean is √50=7.0?? 

Answer 1

mean = np = 50(1/2) = 25

var = npq = 25(1/2) = 12.5

sd = sqrVar = sqr12.5 = about 3.5

1.5sd = about 3.5(1.5) = about 5.3

confidence interval is 25+/-5.3 = (19.7, 30.3)

19 or less heads it's unfair 31 or more heads, it's unfair