SOLUTION: Research on new juvenile delinquents revealed that 38% of them committed another crime. a. What is the probability that of the last 100 new juvenile delinquents put on probation

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Question 948604: Research on new juvenile delinquents revealed that 38% of them committed another crime.
a. What is the probability that of the last 100 new juvenile delinquents put on probation, 30 or more will commit another crime?
b. What is the probability that 40 or fewer of the delinquents will commit another crime?
c. What is the probability that between 30 and 40 of the delinquents will commit another crime?
Answer by reviewermath(1029) About Me  (Show Source):
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Research on new juvenile delinquents revealed that 38% of them committed another crime.
Let X = number of juvenile delinquents in a sample of 100 new juvenile delinquents who will commit another crime
E(X) = np = 100(0.38) = 38
Var(X) = npq = 100(0.38)(1-0.38) = 23.56
X is approximately Normal with mean 38 and variance 23.56
a. What is the probability that of the last 100 new juvenile delinquents put on probation, 30 or more will commit another crime?
Z = %2829.5-38%29%2Fsqrt%2823.56%29 = -1.75
P(Z > -1.75) = 0.96 [Answer]

b. What is the probability that 40 or fewer of the delinquents will commit another crime?

Z = %2840.5-38%29%2Fsqrt%2823.56%29 = 0.515
P(Z < 0.515) = 0.6967 [Answer]
c. What is the probability that between 30 and 40 of the delinquents will commit another crime?
P(Z < 0.515) - P(Z < -1.75) = 0.6967 - (1 - 0.96) = 0.66 [Answer]