Answer:
Given,
Mean = np
= 398*0.033
= 13.134
Standard deviation = sqrt(npq)
= sqrt(398*0.033*(1-0.033))
= 3.5638
a)
P(X > 15) = P(z > (15 - 13.134)/3.5638)
= P(z > 0.52)
= 0.3015318 [since from z table]
= 0.3015
b)
P(X > 30) = P(z > (30 - 13.134)/3.5638)
= P(z > 4.73)
= 0.0000011 [since from z table]
= 0.0000
c)
P(25 < X < 35) = P((25 - 13.134)/3.5638 < (x-u)/s < (35 - 13.134)/3.5638)
= P(3.33 < z < 6.14)
= P(z < 6.14) - P(z < 3.33)
= 1 - 0.9995658 [since from z table]
= 0.0004
d)
P(X > 40) = P(z > (40 - 13.134)/3.5638)
= P(z > 7.54)
= 0
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