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Random samples of size 81 are taken from a population whose mean is 45 and standard deviation is 9. Calculate the probability that a sample mean is less than 42. (round to 4 decimal places)
HINT: When you randomly select a group (n > 1) then you need to re-calculate the standard deviation using the formula:
σ n

Respuesta :

Answer:

Using z table

                         = 0.0013

The probability = 0.0013

Step-by-step explanation:

Given that,

mean = μ = 45

standard deviation = σ   = 9

n=81

μT = μ =45

[tex]\sigma T = \sigma / \sqrt n = 9 / \sqrt81 =1[/tex]

[tex]P(T <42 )\\= P[(T - \mu T ) / \sigma T < (42-45) /1 ]\\\\= P(z <-3 )[/tex]

Using z table

= 0.0013

probability= 0.0013

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