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andreyandreev [35.5K]
2 years ago
10

Sugar canes have lengths X that are normally distributed with mean 365.45 cm and standard deviation 4.9 cm what is the probabili

ty of the length of a randomly selected Cane being between 360 and 370 cm
Mathematics
1 answer:
Gemiola [76]2 years ago
5 0

Answer:

<em>The probability of the length of a randomly selected Cane being between 360 and 370 cm  P(360 ≤X≤370)    = 0.6851</em>

Step-by-step explanation:

<u>step(i)</u>:-

<em>Let 'X' be the random Normal variable</em>

<em>mean of the Population = 365.45</em>

<em>Standard deviation of the population = 4.9 cm</em>

<em>Let X₁ =  360</em>

<em></em>Z= \frac{x-mean}{S.D}= \frac{360-365.45}{4.9}<em></em>

<em>Z₁ = -1.112</em>

<em>Let X₂ =  370</em>

<em></em>Z= \frac{x-mean}{S.D}= \frac{370-365.45}{4.9}<em></em>

<em>Z₂ = 0.911</em>

<u><em>Step(ii</em></u><em>):-</em>

<em>The probability of the length of a randomly selected Cane being between 360 and 370 cm</em>

<em>                   P(x₁≤x≤x₂) =    P(z₁≤Z≤z₂) </em>

<em>                P(360 ≤X≤370)   =    P(-1.11≤Z≤0.911)</em>

<em>                                      =    P(Z≤0.911)-P(Z≤-1.11)</em>

<em>                                      =   0.5 +A(0.911) - (0.5-A(1.11)</em>

<em>                                        =    0.5 +A(0.911) - 0.5+A(1.11)</em>

<em>                                       =     A(0.911) + A(1.11)</em>

<em>                                     =    0.3186 + 0.3665</em>

<em>                                      = 0.6851</em>

<em>The probability of the length of a randomly selected Cane being between 360 and 370 cm  P(360 ≤X≤370)    = 0.6851</em>

<em></em>

<em></em>

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