(Solved) : Probability And Statistics.faq.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?

Expert Answer

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 c.What is the probability that between 30 and 40 of the delinquents will commit another crime?
P(Z

 

(Solved) : Probability And Statistics.faq.question.948603 . . .

The monthly sales of mufflers in the Richmond, VA area follow the normal distribution with a mean of 1200 and a standard deviation of 225. The manufacturer would like to establish inventory levels such that there is only a 5% chance of running out of stock. Where should the manufacturer set the inventory levels?

Expert Answer

The monthly sales of mufflers in the Richmond, VA area follow the normal distribution with a mean of 1200 and a standard deviation of 225. The manufacturer would like to establish inventory levels such that there is only a 5% chance of running out of stock. Where should the manufacturer set the inventory levels?
P(Z > 1.645) = 0.05
Therefore, inventory level should be at least
1.645*sd + mean = 1.645*225 + 1200 ≈ 1571 (rounded up) [Answer]

 

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