Question

Research on new juvenile delinquents put on probation revealed that 38% of them committed an-other 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 from 30 to 40 of the delinquents will commit another crime.

Instruction:
Show all work. For each question (a)-(c) you must
• Neatly draw a normal curve (three of the normal curve in total) •
- Normal curves must be at least 5 lines tall (not too small)
• Label the axis with the appropriate z-values
• Shade the area under the normal curve that corresponds to the probability you are trying to determine
• Show any calculations necessary to determine the final answer • Circle your final answers

Answer 1

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 = = -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 = = 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]