scores on a final exam taken by 1200 students have a bell sh

scores on a final exam taken by 1200 students have a bell shaped distribution with mean=72 and standard deviation=9

a. median score?

b.scores between 63 and 81

c. scores between 72 and 90

d. below 54

Since the data se is large enough, we would consider this as a normal distribution without any loss of accuracy.

For a normal distribution :

Mean = Median = 72 for this case

Now,

WE will try to find out Z-score for each of the above values to determine the percentage of people within the given range.

So,

P (63 < X < 81) = P ( -1 < Z < 1)

= P(Z<1) - P(Z<-1)

= 0.6826

Thus, 68.26% people = 819.12 ~ 820 people would have scores between 63 and 81

(NOTE : Z score = (X - mean) / SD ) So, for X = 63, Z = (63-72)/9 = -1 and so on.

Scores Between 72 and 80

P(72 < X < 90) = P( 0 < Z < 2)

= P(Z <2) - P(Z<0)

= 0.47725

Thus, 47.725% people scored between 72 and 90 = 572.7 ~ 573 people.

P (X < 54) = P(Z<-4)

= 0.00003 %

= 0.036 people ~0

Thus, almost nobody scored below 54

Hope this helps. Ask if you have any doubts. Thanks