In: Statistics and Probability
If μ = 100, σ = 12, and n = 16, then use the t distribution to evaluate the probability ?̅ exceeds 103? Express your answer as a percentage with 3 decimals. |
Solution :
mean = = 100
standard deviation = = 12
n = 16
= = 100
= / n = 12 / 16 = 3
P( > 103) = 1 - P( < 103)
= 1 - P[( - ) / < (103 - 100) / 3]
= 1 - P(z < 1)
Using z table,
= 1 - 0.8413
= 0.1587
The percentage is 15.87%