Answer:
[tex]\bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]
And replacing we got:
[tex]\bar X= 38.91[/tex]
And we can find the bias with this formula:
[tex] Bias= \bar X -\mu[/tex]
And replacing we got:
[tex] Bias = 38.91 -40 = -1.09[/tex]
Step-by-step explanation:
For this problem we know that the random variable of interest follows this distribution:
[tex]X \sim N(\mu =40, \sigma= 10)[/tex]
And we have the following random sample given:
39.2, 45.7, 27.4, 25.9, 25.1, 46.3, 42.9, 49.0, 40.6, 47.0
And we can calculate the sample mean with the following formula:
[tex]\bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]
And replacing we got:
[tex]\bar X= 38.91[/tex]
And we can find the bias with this formula:
[tex] Bias= \bar X -\mu[/tex]
And replacing we got:
[tex] Bias = 38.91 -40 = -1.09[/tex]
