Question

use the normal distribution to approximate the desired probability.
find the probability that in 200 tosses of a fair fie, we will obtain at least 40 fives.

Answer 1

NORMAL APPROXIMATION TO BINOMIAL DISTRIBUTION
the PDF of normal distribution is = 1/σ * √2π * e ^ -(x-u)^2/ 2σ^2
standard normal distribution is a normal distribution with a,
mean of 0,
standard deviation of 1
mean ( np ) = 200 * 0.1667 = 33.34
standard deviation ( √npq )= √200*0.1667*0.8333 = 5.2709
equation of the normal curve is ( Z )= x - u / sd/sqrt(n) ~ N(0,1)

probability that obtain at least 40 fives
P(X < 40) = (40-33.34)/5.2709
= 6.66/5.2709= 1.2635
= P ( Z <1.2635) From Standard Normal Table
= 0.8968
P(X > = 40) = (1 - P(X < 40))
= 1 - 0.8968 = 0.1032