Answer to Question #342653 in Statistics and Probability for Downer

Question #342653

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) = ?


1
Expert's answer
2022-05-23T16:44:02-0400

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"


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