Respuesta :
Answer:
A)
The number of weights of an organ in adult males = 374.85
B)
The percentage of organs weighs between 275 grams and 375
P(275≤x≤375) = 0.6826 = 68%
C)
The percentage of organs weighs between 275 grams and 425
P(275≤x≤375) = 0.8185 = 82%
Step-by-step explanation:
A)
Step(i):-
Given mean of the normal distribution = 325 grams
Given standard deviation of the normal distribution = 50 grams
Given Z- score = 99.7% = 0.997
[tex]Z = \frac{x-mean}{S.D} = \frac{x-325}{50}[/tex]
[tex]0.997 = \frac{x-325}{50}[/tex]
Cross multiplication , we get
[tex]0.997 X 50= x-325[/tex]
x - 325 = 49.85
x = 325 + 49.85
x = 374.85
The number of weights of an organ in adult males = 374.85
Step(ii):-
B)
Let X₁ = 275 grams
[tex]Z_{1} = \frac{x_{1} -mean}{S.D} = \frac{275-325}{50} = -1[/tex]
Let X₂ = 375 grams
[tex]Z_{2} = \frac{x_{2} -mean}{S.D} = \frac{375-325}{50} = 1[/tex]
The probability of organs weighs between 275 grams and 375
P(275≤x≤375) = P(-1≤Z≤1)
= P(Z≤1)- P(Z≤-1)
= 0.5 + A(1) - ( 0.5 - A(-1))
= A(1) + A(-1)
= 2 A(1)
= 2 × 0.3413
= 0.6826
The percentage of organs weighs between 275 grams and 375
P(275≤x≤375) = 0.6826 = 68%
C)
Let X₁ = 275 grams
[tex]Z_{1} = \frac{x_{1} -mean}{S.D} = \frac{275-325}{50} = -1[/tex]
Let X₂ = 425 grams
[tex]Z_{2} = \frac{x_{2} -mean}{S.D} = \frac{425-325}{50} = 2[/tex]
The probability of organs weighs between 275 grams and 425
P(275≤x≤425) = P(-1≤Z≤2)
= P(Z≤2)- P(Z≤-1)
= 0.5 + A(2) - ( 0.5 - A(-1))
= A(2) + A(-1)
= A(2) + A(1) (∵A(-1) =A(1)
= 0.4772 + 0.3413
= 0.8185
The percentage of organs weighs between 275 grams and 425
P(275≤x≤375) = 0.8185 = 82%
