Question

# A random sample of n=81 observations is drawn from a population with a mean equal to...

A random sample of n=81 observations is drawn from a population with a mean equal to 57 and a standard deviation equal to 54, find the probability if x is less than 51, x is greater than 66, and if x falls between 51 and 63

Mean = = 57

Standard deviation = = 54

a)

We have to find P(X < 51)

For finding this probability we have to find z score.

That is we have to find P(Z < - 0.11)

P(Z < - 0.11) = 0.4558 ( Using z table)

b)

We have to find P(X > 66)

For finding this probability we have to find z score.

That is we have to find P(Z > 0.17)

P(Z > 0.17) = 1 - P(Z < 0.17) = 1 - 0.5662 = 0.4338 ( Using z table)

c) We have to find P( 51 < X < 63)

For finding this probability we have to find z score.

That is we have to find P( - 0.11 < Z < 0.11)

P( - 0.11 < Z < 0.11) = P(Z < 0.11) - P(Z < - 0.11) = 0.5442 - 0.4558 = 0.0884

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