A sample of n = 25 observations is drawn from a normal population with and . Find

Answer 1

To find , we need to find the sample mean and standard deviation. Given that the sample size (n) is 25 and the population mean () is 10 and the population standard deviation () is 5, we can calculate as follows:

1. Sample Mean ():

Sample Mean = (sum of all observations) / n

2. Sample Standard Deviation ():

Sample Standard Deviation = sqrt((sum of squared differences from the mean) / (n-1))

Now, let us calculate the sample mean and sample standard deviation using the provided information:

1. Sample Mean:

= 10 (since the sample mean = population mean)

2. Sample Standard Deviation:

= sqrt(((5^2) * 25) / (25-1))
= sqrt((25 * 25) / 24)
= sqrt(625 / 24)
= sqrt(26.0417)
≈ 5.10

Therefore, the sample mean () is 10 and the sample standard deviation () is approximately 5.10.