The formula for a confidence interval for the population mean is:
x̄ ± z*(σ/√n), where x̄ is the sample mean, σ is the population standard deviation, n is the sample size, and z is the z-score associated with the desired confidence level.
For a 90% confidence interval, the z-score is 1.645.
Plugging in the values, we get:
145 ± 1.645*(3.8/√90)
Simplifying the expression:
145 ± 0.9834
We can express the confidence interval as:
(144.0166, 145.9834)
Therefore, we are 90% confident that the true population mean falls within the interval (144.0166, 145.9834).