Pertanyaan

Gunakan tabel distribusi normal Z pada lampiran untuk menyelesaikan soal berikut. Jika Variabel X ∼ N ( 100 , 20 ) , tentukan: a. P ( X ≤ 96 ) b. P ( X > 134 ) c. P ( 120 < X < 167 ) d. P ( 101 < X ≤ 120 ) e. P ( 117 ≤ X < 153 )

Gunakan tabel distribusi normal Z pada lampiran untuk menyelesaikan soal berikut.
Jika Variabel $X \sim N (100, 20)$ , tentukan:

a. $P (X \leq 96)$
b. $P (X > 134)$
c. $P (120 < X < 167)$
d. $P (101 < X \leq 120)$
e. $P (117 \leq X < 153)$

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O. Rahmawati

Master Teacher

Mahasiswa/Alumni UIN Sunan Gunung Djati Bandung

Jawaban terverifikasi

Pembahasan

a. b. c. d. e.

a. P left parenthesis X less or equal than 96 right parenthesis

$table attributes columnalign right center left columnspacing 0px end attributes row cell P left parenthesis X end cell less or equal than cell 96 right parenthesis equals P open parentheses Z less or equal than fraction numerator 96 minus 100 over denominator 20 end fraction close parentheses end cell row blank blank cell equals P open parentheses Z less or equal than negative 0 comma 2 close parentheses equals P left parenthesis Z less than negative 0 comma 2 right parenthesis equals 0 comma 4207 end cell end table$

b. P left parenthesis X greater than 134 right parenthesis

$table attributes columnalign right center left columnspacing 0px end attributes row cell P left parenthesis X end cell greater than cell 134 right parenthesis equals P open parentheses Z less than fraction numerator 134 minus 100 over denominator 20 end fraction close parentheses end cell row blank blank cell equals P left parenthesis Z less than 1 comma 7 right parenthesis equals 0 comma 9554 end cell row blank blank blank end table$

c. P left parenthesis 120 less than X less than 167 right parenthesis

$table attributes columnalign right center left columnspacing 0px end attributes row cell P left parenthesis 120 end cell less than cell X less than 167 right parenthesis equals P open parentheses fraction numerator 120 minus 100 over denominator 20 end fraction less than Z less than fraction numerator 167 minus 100 over denominator 20 end fraction close parentheses end cell row blank blank cell space space space space space equals P left parenthesis 1 less than Z less than 3 comma 35 right parenthesis equals P left parenthesis Z greater than 1 right parenthesis plus P left parenthesis Z less than 3 comma 35 right parenthesis equals 0 comma 8413 plus 0 comma 9996 equals 1 comma 8409 end cell end table$

d. P left parenthesis 101 less than X less or equal than 120 right parenthesis

$table attributes columnalign right center left columnspacing 0px end attributes row cell P left parenthesis 101 end cell less than cell X less or equal than 120 right parenthesis equals P open parentheses fraction numerator 101 minus 100 over denominator 20 end fraction less than Z less or equal than fraction numerator 120 minus 100 over denominator 20 end fraction close parentheses end cell row blank blank cell equals P left parenthesis 0 comma 05 less than Z less or equal than 1 right parenthesis equals P left parenthesis 0 comma 05 less than Z less than 1 right parenthesis equals P left parenthesis Z greater than 0 comma 05 right parenthesis plus P left parenthesis Z less than 1 right parenthesis equals 0 comma 5199 plus 0 comma 8413 equals 1 comma 3612 end cell end table$

e. P left parenthesis 117 less or equal than X less than 153 right parenthesis

$table attributes columnalign right center left columnspacing 0px end attributes row cell P left parenthesis 117 end cell less or equal than cell X less than 153 right parenthesis equals P open parentheses fraction numerator 117 minus 100 over denominator 20 end fraction less or equal than Z less than fraction numerator 153 minus 100 over denominator 20 end fraction close parentheses end cell row blank blank cell equals P left parenthesis 0 comma 85 less or equal than Z less than 2 comma 65 right parenthesis equals P left parenthesis 0 comma 85 less than Z less than 2 comma 65 right parenthesis equals P left parenthesis Z greater than 0 comma 85 right parenthesis plus P left parenthesis Z less than 2 comma 65 right parenthesis equals 0 comma 8023 plus 0 comma 9960 equals 1 comma 7893 end cell end table$

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