A normal population has mean 100 and variance 25. How large must the random sample be if you want the standard error of the sample average to be 1.5? (also calculate the probability of the average exceeds 105 based on 16 observations from this normal population)
Solution :
Given that ,
mean = = 100
standard deviation = = 5
n = 16
_{} = = 100 and
_{} = 1.5
P( > 105) = 1 - P( < 105)
= 1 - P(( - _{} ) / _{} < (105 - 100) / 1.5)
= 1 - P(z < 3.33)
= 1 - 0.9996 Using standard normal table.
= 0.0004
Probability = 0.0004
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