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)=(43)(0.10)3(10.10)43=0.0036P(X=3)=\dbinom{4}{3}(0.10)^{3}(1-0.10)^{4-3}=0.0036

ii.


P(X=4)=(74)(0.10)4(10.10)74P(X=4)=\dbinom{7}{4}(0.10)^{4}(1-0.10)^{7-4}

=0.0025515=0.0025515

iii.


P(X7)=P(X=7)+P(X=8)P(X\ge7)=P(X=7)+P(X=8)

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

=(107)(0.10)7(10.10)107=\dbinom{10}{7}(0.10)^{7}(1-0.10)^{10-7}

+(108)(0.10)8(10.10)108+\dbinom{10}{8}(0.10)^{8}(1-0.10)^{10-8}

+(109)(0.10)9(10.10)109+\dbinom{10}{9}(0.10)^{9}(1-0.10)^{10-9}

+(1010)(0.10)10(10.10)1010+\dbinom{10}{10}(0.10)^{10}(1-0.10)^{10-10}

=0.0000091216=0.0000091216

iv.


P(5X7)=P(X=5)+P(X=6)P(5\le X\le7)=P(X=5)+P(X=6)

+P(X=7)=(125)(0.10)5(10.10)125+P(X=7)=\dbinom{12}{5}(0.10)^{5}(1-0.10)^{12-5}

+(126)(0.10)6(10.10)126+\dbinom{12}{6}(0.10)^{6}(1-0.10)^{12-6}

+(127)(0.10)7(10.10)127+\dbinom{12}{7}(0.10)^{7}(1-0.10)^{12-7}

=0.00378811145+0.00049105148=0.00378811145+0.00049105148

+0.00004676681=0.00432592974+0.00004676681=0.00432592974


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