Respuesta :
Answer:
The probability of the length of a randomly selected Cane being between 360 and 370 cm P(360 ≤X≤370) = 0.6851
Step-by-step explanation:
step(i):-
Let 'X' be the random Normal variable
mean of the Population = 365.45
Standard deviation of the population = 4.9 cm
Let X₁ = 360
[tex]Z= \frac{x-mean}{S.D}= \frac{360-365.45}{4.9}[/tex]
Z₁ = -1.112
Let X₂ = 370
[tex]Z= \frac{x-mean}{S.D}= \frac{370-365.45}{4.9}[/tex]
Z₂ = 0.911
Step(ii):-
The probability of the length of a randomly selected Cane being between 360 and 370 cm
P(x₁≤x≤x₂) = P(z₁≤Z≤z₂)
P(360 ≤X≤370) = P(-1.11≤Z≤0.911)
= P(Z≤0.911)-P(Z≤-1.11)
= 0.5 +A(0.911) - (0.5-A(1.11)
= 0.5 +A(0.911) - 0.5+A(1.11)
= A(0.911) + A(1.11)
= 0.3186 + 0.3665
= 0.6851
The probability of the length of a randomly selected Cane being between 360 and 370 cm P(360 ≤X≤370) = 0.6851
