Question

Find the probability that in 200 tosses of a fair six-sided die, a five will be obtained at most 40 times.

Answer 1

91.31%

Explanation:

The first step to this is using the binomial distribution which is = np or n (1-p)

The binomial distribution will be n=200 and p=1/6;

np=200/6=33.33

n(1-p)=200*5/6=166.67

Both n(1-p) and np are much higher than 5,

Therefore will use it with a normal distribution given μ=np and σ²=np(1-p) and P(x≤40) is accurate by P(Y≤40.5)

Therefore

P(Y≤40.5) = P(z≤(40.5-μ)/σ) = P(z≤1.36) = 0.9131 = 91.31%