2 2 An exam is administered to 20 high school students chose

2. (+2) An exam is administered to 20 high school students, chosen randomly from within a large school district. Suppose that, if everyone in the school district were to take the exam, scores would follow a normal distribution, with mean . 69 and standard deviation . 18. What is the probability that the average score for these 20 students is more than 5 percentage points away from the population average (i.e. less than .64 or greater than .74)?

Solution

standard error = sd/sqrt(n) =0.18/sqrt(20) =0.0402

z value for 0.64, z=( 0.64- 0.69)/0.0402 =-1.24

z value for 0.74, z=( 0.74- 0.69)/0.0402 = 1.24

P( 0.64 <x<0.74)= P( -1.24<z<1.24)

P(z <1.24)- P(z <-1.24)= 0.8925 - 0.1075

= 0.7850