14)i) P(X > 30000)
= P((X -
)/
> (30000 -
)/
)
= P(Z > (30000 - 30000)/3000)
= P(Z > 0)
= 1 - P(Z < 0)
= 1 - 0.5 = 0.5
Expected no of students = 500 * 0.5 = 250
ii) P(27000 < X < 33000)
= P((27000 - 30000)/3000 < Z < (33000 - 30000)/3000)
= P(-1 < Z < 1)
= P(Z < 1) - P(Z < -1)
= 0.8413 - 0.1587
= 0.6826
Expected no of students = 500 * 0.6826 = 341.3
iii) P(24000 < X < 30000)
= P((24000 - 30000)/3000 < Z < (30000 - 30000)/3000)
= P(-2 < Z < 0)
= P(Z < 0) - P(Z < -2)
= 0.5 - 0.0228
= 0.4772
Expected no of students = 500 * 0.4772 = 239
Option - B) (i) and (iii) are correct statements but not (ii).
15) For section - 1
z-score = (x -
)/
= (84 - 75)/7 = 1.2857
For section - 2
z-score = (x -
)/
= (75 - 60)/8 = 1.875
Option - C) (i), (ii), and (iii) all are correct statements.
16) P(Z > 1.75)
= 1 - P(Z < 1.75)
= 1 - 0.9599
= 0.0401
Option - A is correct
17) P(X < 45000)
= P((X -
)/
< (45000 -
)/
)
= P(Z < (45000 - 50000)/4000)
= P(Z < -1.25)
= 0.1056
Expected no of students = 500 * 0.1056 = 53
18) P(-2 < Z < 2)
= P(Z < 2) - P(Z < -2)
= 0.9772 - 0.0228
= 0.9544 = 95.44%
Option - A is correct
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