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After a million measurements of thing x, we find a sample mean of 50.36 and standard deviation of 1.58. What chance, in percent (0-100) does the next measurement have of being 2 standard deviations from the mean? Do not include the percent sign.

Respuesta :

Answer:

68

Step-by-step explanation:

Given:

sample mean u = 50.36

standard deviation δ = 1.58

Assuming measurements x follows a normal distribution as follows:

   X - N ( u , δ^2 )      -- >    X - N ( 50.36 , 2.4964 )

The probability of next measurement being 2 δ from mean u :

P ( u - δ < X < u + δ )  -----> P ( 48.78 < X < 51.94 )

Compute z-score and corresponding probability values:

P ( 48.78 < X < 51.94 ) = P ( (48.78 - 50.36) / 1.58 <  z  < (51.94 - 50.36) / 1.58 )

P ( 48.78 < X < 51.94 ) = P ( -1 < z < 1 ) = 0.68

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