Question 5 (6 marks total) A survey of local car dealers revealed that 64% of al

Question

Question 5 (6 marks total) A survey of local car dealers revealed that 64% of all cars sold last month had CD players, 28% had alarm systems, and 22% had both CD players and alarm systems. What is the probability that one of these cars selected at random had neither a player nor an alarm system? (2 marks) CD a. If 10 of these cars are randomly selected, what is the probability that exactly half of them had alarm systems? [Hint: Binomial distribution] (2 marks) b. ing a CD player and an alarm system disjoint (mutually exclusive) events? Explain. (2 marks) Question 6 (10 marks total) Suppose that the survival time (in months) for patients on a certain drug is normally distributed with a mean of 31.1 months and a standard deviation of 14.8 months. Find the probability that a randomly selected patient on the drug survives for no more than one year. (3 marks) a. b. Find the interquartile range (IQR) of the survival times. (3 marks) c. If 40 patients on the drug are randomly selected, what is the probability that their mean survival time is more than two years? (4 marks)

Explanation / Answer

Question 5 :

P(A) = probability that the car sold had cd player = 0.64

P(B)= prob that the car had alarm system = 0.28

P( A intersection B) = 0.22

a. P(A U B) = P(A) + P(B) - P(A intersection B) = 0.64+0.28-0.22 = 0.7

P [ the car had either cd player or alarm system ] = 0.7

P [ the cr had neither cd player nor alarm system ] = 1-0.7 = 0.3

b. n= 10

p= prob of having alarm system = 0.28

X = no of cars having alarm system

X follows binomial distribution

P[ X=5] = 10C5 *0.285 *(1-0.28)5 = 0.08391762413

d. having alarm system and cd player is not disjoint system

because P [ A and B ] = 0.22

it is not zero.

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