b. We have a sample mean = 5, sample size n = 8. Since 8 is very small we use the t-distribution to estimate sample mean distributions, with df = n-1 = 7.

The standard error of our sample mean is sd/sqrt(n)

= 1.3/sqrt(7)

= 0.491353815

So our t-stat is given by (sample mean - population mean) / standard error

t = (5-4.2) / 0.49

= 1.628

Therefore, the probability our sample mean is greater than 5 will be one minus the probability it is less, which is