Question

Suppose a random variable has population mean -147 and population standard deviation 34.50. What is the lower and upper values of the probability interval containing 95% of the sample means of sample size n = 112?

Lower =  
Upper =  
(Round to 3 decimal places.)

Answer 1

Answer 2

The standard error of the mean (SEM) can be calculated as:

SEM = σ/√n

where σ is the population standard deviation and n is the sample size.

In this case, σ = 34.50 and n = 112, so:

SEM = 34.50/√112 ≈ 3.253

To find the lower and upper values of the probability interval containing 95% of the sample means, we need to calculate the margin of error (ME) and then add and subtract it from the sample mean.

ME = z*SEM

where z is the z-score corresponding to the desired level of confidence. For a 95% confidence level, z = 1.96.

ME = 1.96*3.253 ≈ 6.37

So the lower and upper values of the probability interval containing 95% of the sample means are:

Lower = -147 - 6.37 = -153.37 Upper = -147 + 6.37 = -140.63

Therefore, we can say that with 95% confidence, the true population mean is between -153.37 and -140.63.