Respuesta :
Answer:
The probability of spending between 4 and 7 days in recovery
P(4≤x≤7) = 0.5445
Step-by-step explanation:
Step(i):-
Given mean of the Population μ = 5.3 days
Given standard deviation of the population 'σ' = 2 days
Let 'X' be the random variable in normal distribution
Let x₁ = 4
[tex]Z_{1} = \frac{x_{1}-mean }{S.D} = \frac{4-5.3}{2} = -0.65[/tex]
Let x₂ = 7
[tex]Z_{2} = \frac{x_{2}-mean }{S.D} = \frac{7-5.3}{2} = 0.85[/tex]
Step(ii):-
The probability of spending between 4 and 7 days in recovery
P(4≤x≤7) = P(-0.65≤Z≤0.85)
= P(Z≤0.85) - P(Z≤-0.65)
= 0.5 + A( 0.85) - ( 0.5 - A(-0.65)
= 0.5 + A( 0.85) - 0.5 +A(0.65) ( ∵A(-0.65) = A(0.65)
= A(0.85) + A(0.65)
= 0.3023 + 0.2422
= 0.5445
Final answer:-
The probability of spending between 4 and 7 days in recovery
P(4≤x≤7) = 0.5445
