A distribution of measurements is relatively mound-shaped with a mean of 40 and a standard deviation of 15. Use this information to find the proportion of measurements in the given interval. between 25 and 55

The proportion of measurements between 25 and 55

P( 25 ≤ X≤ 55) = 0.6826

Step-by-step explanation:

Step(i):-

Given that the mean of the Population = 40

Given that standard deviation of the Population = 15

Let 'x' be the random variable in normal distribution

Let 'X' = 25

Let 'X' = 55

Step(ii):-

The probability that between 25 and 55

P( 25 ≤ X≤ 55) = P( -1≤z≤1)

                       = A(1) - A(-1)

                      = A(1) + A(1)

                     = 2 × A(1)

                    = 2× 0.3413

                   = 0.6826

The proportion of measurements between 25 and 55

P( 25 ≤ X≤ 55) = 0.6826

Final -

The proportion of measurements between 25 and 55

P( 25 ≤ X≤ 55) = 0.6826

the answer is 8/21

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