5-

To open a combination lock, you turn the dial to the right and stop at a number; then you turn it to the left and stop at a second number. Finally, you turn the dial back to the right and stop at a third number. If you used the correct sequence of numbers, the lock opens. If the dial of the lock contains 10 numbers, 0 through 9, determine the number of different combinations possible for the lock. Note: The same number can be reused consecutively.

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Isle Royale, an island in Lake Superior, has provided an important study site of wolves and their prey. Of special interest is the study of the number of moose killed by wolves. In the period from 1958 to 1974, there were 296 moose deaths identified as wolf kills. The age distribution of the kills is as follows.

Age of Moose in Years Number Killed by Wolves

Calf (0.5 yr) 113

1-5 48

6-10 72

11-15 61

16-20 2

(a) For each age group, compute the probability that a moose in that age group is killed by a wolf. (Round your answers to three decimal places.)

0.5

1-5

6-10

11-15

16-20

(b) Consider all ages in a class equal to the class midpoint. Find the expected age of a moose killed by a wolf and the standard deviation of the ages. (Round your answers to two decimal places.)

=

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9-

A stationary store has decided to accept a large shipment of ball-point pens if an inspection of 15 randomly selected pens yields no more than two defective pens.

(a) Find the probability that this shipment is accepted if 10% of the total shipment is defective. (Use 3 decimal places.)

(b) Find the probability that this shipment is not accepted if 20% of the total shipment is defective. (Use 3 decimal places.)