The weight of an organ in adult males has a bell shaped distribution with a mean of 325 grams and a standard deviation of 50 grams. (A) about 99.7% of organs will be between what weights? (B) what percentage of organs weighs between 275 grams and 375? (C) what percentage of organs weighs between 275 grams and 425 grams?

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

Cross multiplication , we get

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

Let X₂ = 375 grams

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

Let X₂ = 425 grams

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%

b

step-by-step explanation:

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