Question

In: Statistics and Probability

Suppose samples of size 100 are drawn randomly from a population of size 1000 and the...

Suppose samples of size 100 are drawn randomly from a population of size 1000 and the population has a mean of 20 and a standard deviation of 5. What is the probability of observing a sample mean equal to or greater than 21?

Expert Solution

Solution:

Given that,

= 20

= 5

n = 100

So,

= 20

= ( / $\sqrt$ n) = (5/ $\sqrt$ 100 ) = 0.5

p ( 21 )

= 1 - p ( 21 )

= 1 - p ( - / ) ? ( 21- 20 / 0.5)

= 1 - p ( z ? 1 /0.5)

= 1 - p ( z ? 2)

Using z table

= 1 - 0.9772

= 0.0228

Probability = 0.0228

orchestra answered 2 years ago

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