To solve this problem, we use the t statistic. The z score is calculated as:
z = (x – u) / s
where x is the sample value = 53 and 77, u is the mean score = 65 while s is the standard deviation = 4
when x = 53
z = (53 – 65) / 4 = -3
From the standard distribution tables, the p value at z = -3 is:
P (z=-3) = 0.0013
when x = 77
z = (77 – 65) / 4 = 3
From the standard distribution tables, the p value at z = 3 is:
P (z=3) = 0.9987
The percentage P between the two would be the difference:
P (53 < x < 77) = 0.9987 – 0.0013 = 0.9974
Answer:
0.9974 or 99.74%
