Math

STA2023 TEST 3 CHAPTERS 5 and 6

NAME:_________________________

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A survey of durability among 1500 car batteries shows that the distribution of the life of batteries is normal with a mean at about 2 years and a standard deviation of 4 months.

1) Compute the probability that a randomly selected battery last less than 23 months

2) Compute the probability that a randomly selected battery last more than 26 months

3) Compute the probability that a battery last between 20 and 26 months.

4) Determine the cut off durability to offer at most 1 % full replacement for customer satisfaction in the battery sales.

5) Determine the probability that a set of nine batteries last more than 26 months.

6) Determine the probability that a set of 900 last more than 26 months

7) If in the group of 900 batteries the probability to have a faulty battery is 0.20, compute the probability to have in the group about 250 faulty batteries

8) Determine whether the distribution of Durability for the batteries is Normal or not. Justify your answer

9) a) Determine whether the distribution is a PDF,

b) justify why or why not,

c) compute its average.

X 0 1 1 2

P(X) 0.5 3/10 6/20 0.2

10) Compute the average of defective parts if in a group of 17 the probability to obtain a defective part is 30 %

353025201510

99.9

99

95

90

80

70

60

50

40

30

20

10

5

1

0.1

Mean23.35

StDev3.644

N230

AD0.389

P-Value0.382

Durability A

P

e

r

c

e

n

t

Probability Plot of Durability A

Normal