3. A sample of 25 outcomes is taken from a population that is Normal(50, 3). The

Question

3. A sample of 25 outcomes is taken from a population that is Normal(50, 3). The mean of this particular sample is found to be 48.5. Find the probability that one particular observation in this sample is less than 48.5. a.) 0.0062 b.) 0.3085 c.) 0.6915 3. A sample of 25 outcomes is taken from a population that is Normal(50, 3). The mean of this particular sample is found to be 48.5. Find the probability that one particular observation in this sample is less than 48.5. a.) 0.0062 b.) 0.3085 c.) 0.6915

Explanation / Answer

Mean ( u ) =48.5
Standard Deviation ( sd )=3/ Sqrt ( 25 ) = 0.6
Number ( n ) = 25
Normal Distribution = Z= X- u / (sd/Sqrt(n) ~ N(0,1)                                      
P(X < 48.5) = (48.5-50)/3/ Sqrt ( 25 )
= -1.5/0.6= -2.5
= P ( Z <-2.5) From Standard NOrmal Table
= 0.0062                  

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