Binomial and normal distributions
Answers are for parents and teachers.
1
A coin is tossed 5 times. Find the probability of exactly two heads.
C(5, 2)/2⁵ = 10/32 = 5/16.
2
A seed germinates with probability 0.9. Four seeds are sown. Find the probability that all germinate.
0.9⁴ = 0.6561.
3
Make the binomial distribution table for n = 3, p = 0.4 and check the sum.
q = 0.6: P(0) = 0.216; P(1) = 3 · 0.4 · 0.36 = 0.432; P(2) = 3 · 0.16 · 0.6 = 0.288; P(3) = 0.064. The sum is 1.
4
Test scores are normally distributed with a = 100 and σ = 15. In which interval do about 95 % of the results lie?
a ± 2σ: from 70 to 130.
5
Why, for p = 0.5, is the largest probability of the binomial distribution at the centre?
For p = q we have P(n, m) = C(n, m)/2ⁿ and C(n, m) = C(n, n − m): the table is symmetric and the binomial coefficients are largest in the middle (Pascal’s triangle).