Diketahui variabel acak, berdistribusi normal, . Tentukan besar peluang berikut!, g.,

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Baca Juga :  , Conversation 2

PERTANYAAN :


Diketahui variabel acak X berdistribusi normal N open parentheses 15 comma space 5 close parentheses. Tentukan besar peluang berikut! 

g. straight P open parentheses 8 less than X less than 17 close parentheses  

Jawaban

nilai peluang dari straight P open parentheses 8 less than X less than 17 close parentheses adalah 0 comma 5846


Pembahasan

Jawaban yang benar untuk pertanyaan tersebut adalah 0 comma 5846

Ingat! 

Transformasi variabel acak X tilde N open parentheses mu comma space sigma close parentheses menjadi Z tilde N open parentheses 0 comma space 1 close parentheses menggunakan rumus 

Z equals fraction numerator X minus mu over denominator sigma end fraction 

Perhatikan perhitungan berikut ini! 

Diketahui:

table attributes columnalign right center left columnspacing 0px end attributes row cell x subscript 1 end cell equals 8 row cell x subscript 2 end cell equals 17 row mu equals 15 row sigma equals 5 end table 

Sehingga 

table attributes columnalign right center left columnspacing 0px end attributes row cell z subscript 1 end cell equals cell fraction numerator 8 minus 15 over denominator 5 end fraction end cell row blank equals cell fraction numerator negative 7 over denominator 5 end fraction end cell row blank equals cell negative 1 comma 4 end cell row blank blank blank row cell z subscript 2 end cell equals cell fraction numerator 17 minus 15 over denominator 5 end fraction end cell row blank equals cell 2 over 5 end cell row blank equals cell 0 comma 4 end cell end table 

Dengan menggunakan tabel normal baku diperoleh 

table attributes columnalign right center left columnspacing 0px end attributes row cell straight P open parentheses 8 less than X less than 17 close parentheses end cell equals cell straight P open parentheses negative 1 comma 4 less than Z less than 0 comma 4 close parentheses end cell row blank equals cell straight P open parentheses Z less than 0 comma 4 close parentheses minus straight P open parentheses straight Z less than negative 1 comma 4 close parentheses end cell row blank equals cell straight P open parentheses Z less than 0 comma 4 close parentheses minus open square brackets 1 minus straight P open parentheses straight Z less than 1 comma 4 close parentheses close square brackets end cell row blank equals cell straight P open parentheses Z less than 0 comma 4 close parentheses plus straight P open parentheses straight Z less than 1 comma 4 close parentheses minus 1 end cell row blank equals cell 0 comma 6654 plus 0 comma 9192 minus 1 end cell row blank equals cell 0 comma 5846 end cell end table 

Catatan: 
Untuk menentukan nilai dari straight P open parentheses Z less than 0 comma 4 close parentheses, perhatikan bahwa 0 comma 4 equals 0 comma 4 plus 0. Pada tabel distribusi Z perhatikan angka 0 comma 4 pada kolom paling kiri lalu tarik garis ke kanan dan pada baris paling atas perhatikan angka 0 kemudian tarik garis ke bawah. Pada pertemuan kedua garis di dapatkan nilai straight P open parentheses Z less than 0 comma 4 close parentheses equals 0 comma 6654. Dengan cara yang sama untuk mendapatkan nilai straight P open parentheses Z less than 1 comma 4 close parentheses

Baca Juga :  , "As you know on every 10 November we all celebrate Heroes Days. Why do you think the Heroes Day took that special date to commemorate our heroes sacrifice? Discuss with your partners and come to a conclusion why the date has become special. After that, read through the passage and check whether your conclusion is the same as the reason stated in the text.", On 10 November, Indonesia celebrates Hari Pahlawan or Heroes Day in , of the Battle of Surabaya which started on that very date in the year 1945. The bloody battle took place because Indonesians refused to surrender their weaponry to British army. British Army at that time was part of the Allied Forces. The , Bung Tomo is the well-known revolutionary leader who played a very important role in this battle., It all started because of a misunderstanding between British troops in Jakarta and those in Surabaya, under the command of Brigadier A.W.WS. Mallaby. Brigadier Mallaby already had an agreement with Governor of East Java Mr. Surya. The agreement stated that British would not ask Indonesian troops and militia to surrender their weapons., However, a British plane from Jakarta dropped leaflets all over Surabaya. The leaflet told Indonesians to do otherwise on 27 October 1945. This action , the Indonesian troops and militia leaders because they felt betrayed., On 30 October 1945, Brigadier Mallaby was killed as he was approaching the British troops’ post near Jembatan Merah or Red Bridge, Surabaya. There were many reports about the death, but it was widely believed that the Brigadier was murdered by Indonesian militia. Looking at this situation, Lieutenant General Sir Philip Christison brought in , to , the city., In the early morning of 10 November 1945, British troops began to advance into Surabaya with cover from both naval and air bombardment. Although the Indonesians defended the city heroically, the city was conquered within 3 days and the whole battle lasted for 3 weeks. In total, between 6,000 and 16,000 Indonesians died while casualties on the British side were about 600 to 2000., Battle of Surabaya caused Indonesia to lose , which , the country’s independence struggle. However, the battle provoked Indonesian and international mass to rally for the country’s independence which made this battle especially important for Indonesian national revolution.

 

Dengan demikian, nilai peluang dari straight P open parentheses 8 less than X less than 17 close parentheses adalah 0 comma 5846


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Baca Juga :  4.

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