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The Head teacher needs a report that; indicate the sanitation budget, analyses a 3-month trends in student health by and estimates cases in July, estimate the expected daily absenteeism caused by sanitation-related illnesses.

Mathematics

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3 parts
i

2,240,000 Shs2,240,000 \text{ Shs}

ii

23 kesi23 \text{ kesi}

iii

1.65 wanafunzi1.65 \text{ wanafunzi}

Step-by-step solution

3 steps

Huu hapa ni ripoti kwa Mwalimu Mkuu, ikijumuisha mahitaji yaliyotajwa:

Part i

Bajeti ya Usafi

Bajeti ya jumla ya usafi iliyokokotolewa hapo awali ni:

2,240,000 Shs\boxed{2,240,000 \text{ Shs}}

Part ii

23 kesi23 \text{ kesi}

Uchambuzi wa Mwenendo wa Afya ya Wanafunzi kwa Miezi 3 na Makadirio ya Kesi mwezi Julai

  1. Changanua mwenendo wa kesi za kutohudhuria shule kutokana na magonjwa yanayohusiana na usafi kwa miezi mitatu iliyopita (Aprili, Mei, Juni).

    • Aprili: Kesi 28
    • Mei: Kesi 19 (Kupungua kutoka Aprili)
    • Juni: Kesi 21 (Kuongezeka kidogo kutoka Mei) Mwenendo unaonyesha kupungua kwa jumla kutoka Aprili hadi Mei, kisha kuongezeka kidogo mwezi Juni. Kwa ujumla, kutoka Januari (kesi 36) hadi Juni (kesi 21), kuna upungufu wa jumla wa kesi, kuashiria uboreshaji wa afya ya wanafunzi.

  2. Kadiria idadi ya kesi mwezi Julai.

    Tunatumia wastani wa kesi za miezi mitatu iliyopita (Aprili, Mei, Juni) kukadiria Julai:

    Wastani=28+19+213=683≈22.67\text{Wastani} = \frac{28 + 19 + 21}{3} = \frac{68}{3} \approx 22.67

    Kwa hiyo, idadi inayokadiriwa ya kesi mwezi Julai ni takriban 23 kesi\boxed{23 \text{ kesi}}.

Part iii

1.65 wanafunzi1.65 \text{ wanafunzi}

Makadirio ya Kutohudhuria Shule Kila Siku Kunakosababishwa na Magonjwa Yanayohusiana na Usafi

  1. Kokotoa thamani inayotarajiwa (expected value) ya idadi ya wanafunzi wasiohudhuria shule.

    Thamani inayotarajiwa E(X)E(X) inakokotolewa kwa kutumia fomula E(X)=∑x⋅P(x)E(X) = \sum x \cdot P(x):

    E(X)=(0×0.20)+(1×0.30)+(2×0.25)+(3×0.15)+(4×0.10)E(X) = (0 \times 0.20) + (1 \times 0.30) + (2 \times 0.25) + (3 \times 0.15) + (4 \times 0.10) E(X)=0+0.30+0.50+0.45+0.40E(X) = 0 + 0.30 + 0.50 + 0.45 + 0.40 E(X)=1.65E(X) = 1.65

    Kwa hiyo, makadirio ya kutohudhuria shule kila siku kunakosababishwa na magonjwa yanayohusiana na usafi ni 1.65 wanafunzi\boxed{1.65 \text{ wanafunzi}}.

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