The sample mean estimate, xbar = μ, the mean of the population, and the sample mean estimate for the standard error is σ/sqrt(n) , where σ is the population standard deviation and n is the sample size:
xbar = 514 and s = 118/sqrt(65) = 14.64
In order to figure out the probability of the sample average being between 500 and 520, we need to figure out the area under the normal curve between the z values represented by those limits. You can also just use the cdf for the normal dist inputting the mean, standard error and the limits.
Using the chart requires finding the z values: the lower z = (500-514)/14.64 = -.9565
the upper z = (520-514)/14.64 = .4099
Area = probability of being between these limits = left area(.41) - left area(=.97) = .6591 - .1685 = 49%
Take care.
