Finding the number of students who scored 50 and above:

To find the number of students who scored 50 and above, we need to calculate the z-score for 50 using the formula z = (x - μ) / σ, where x is the score we want to find the z-score for, μ is the mean, and σ is the standard deviation.

z = (50 - 42) / 24
z = 0.33

Using a z-table, we find that the probability of a z-score of 0.33 or higher is 0.3707. This means that approximately 37.07% of the students scored 50 or higher.

Therefore, the number of students who scored 50 and above is:

0.3707 x 1000 = 370.7

Rounding this off to the nearest whole number, we get:

371 students scored 50 and above.

Finding the number of students lying between 30 and 54:

To find the number of students lying between 30 and 54, we need to calculate the z-scores for both 30 and 54 using the formula z = (x - μ) / σ.

For 30:

z = (30 - 42) / 24
z = -0.5

For 54:

z = (54 - 42) / 24
z = 0.5

Using a z-table, we find that the probability of a z-score of -0.5 or lower is 0.3085, and the probability of a z-score of 0.5 or lower is 0.6915.

Therefore, the probability of a student scoring between 30 and 54 is:

0.6915 - 0.3085 = 0.383

Multiplying this probability by the total number of students, we get:

0.383 x 1000 = 383

Therefore, 383 students scored between 30 and 54.

Finding the value of score exceeded by the top 100 students:

To find the value of score exceeded by the top 100 students, we need to find the z-score that corresponds to the top 100 students. We can do this by using the formula z = (x - μ) / σ, where x is the score we want to find the z-score for, μ is the mean, and σ is the standard deviation.

Using a z-table, we find that the z-score that corresponds to the top 100 students is approximately 1.28.

Therefore, the score exceeded by the top 100 students is:

x = μ + zσ
x = 42 + 1.28(24)
x = 72.72

Therefore, the score exceeded by the top 100 students is 72.72.