Answer to Question #342653 in Statistics and Probability for Downer

Question

Solve the following problems by using Binomial formula:

i. If n = 4 and p = 0.10, P(X = 3) = ?

ii. If n = 7 and p = 0.10, P(X = 4) = ?

iii. If n = 10 and p = 0.10, P(X  7) = ?

iv. If n = 12 and p = 0.10, P(5  X  7) = ?

Answer 1

i.

$$P(X=3)=\dbinom{4}{3}(0.10)^{3}(1-0.10)^{4-3}=0.0036$$

ii.

$$P(X=4)=\dbinom{7}{4}(0.10)^{4}(1-0.10)^{7-4}$$

$$=0.0025515$$

iii.

$$P(X\ge7)=P(X=7)+P(X=8)$$

$$+P(X=9)+P(X=10)$$

$$=\dbinom{10}{7}(0.10)^{7}(1-0.10)^{10-7}$$

$$+\dbinom{10}{8}(0.10)^{8}(1-0.10)^{10-8}$$

$$+\dbinom{10}{9}(0.10)^{9}(1-0.10)^{10-9}$$

$$+\dbinom{10}{10}(0.10)^{10}(1-0.10)^{10-10}$$

$$=0.0000091216$$

iv.

$$P(5\le X\le7)=P(X=5)+P(X=6)$$

$$+P(X=7)=\dbinom{12}{5}(0.10)^{5}(1-0.10)^{12-5}$$

$$+\dbinom{12}{6}(0.10)^{6}(1-0.10)^{12-6}$$

$$+\dbinom{12}{7}(0.10)^{7}(1-0.10)^{12-7}$$

$$=0.00378811145+0.00049105148$$

$$+0.00004676681=0.00432592974$$