Narinderjit Singh - UTP Assignment Probability and Statistics – September 2012

ASSIGNMENT (10%)

Probability and Statistics

Deadline: 19/12/2012

1. Diameters of 36 rivets heads, in 0.012 inch, are given as below

6.72 6.77 6.82 6.70 6.78 6.70 6.62 6.75 6.66

6.66 6.64 6.76 6.73 6.80 6.72 6.76 6.76 6.68

6.66 6.62 6.72 6.76 6.70 6.78 6.76 6.67 6.70

6.72 6.74 6.81 6.79 6.78 6.66 6.76 6.76 6.72

a. Compute the sample mean and sample standard deviation.b. Construct the relative frequency histogram of the data by using the interval

[6.60 – 6.65), [6.65 – 6.70), ……………………….

2. A town has 2 fire engines operating independently. The probability that a specific engine is available when needed is 0.96.

a. What is the probability that neither is available when needed?b. What is the probability that a fir engine is available when needed?

3. Select at random 6 books from a bookshelf that consists of 7 Mathematical books and 8 Physics books. Find the probability that

a. two kinds of books with the same amount of items each will be selected,b. only one kind of books will be selected,c. both kinds of books will be selected,d. six (6) books of Physics are selected given that only one kind of books is

selected.

4. Police plan to enforce speed limits by using radar traps at 4 different locations within the city limits. The radar traps at each of the locations L1, L2, L3, L4 are operated 40%, 30%, 20%, and 30% of the time.

a. If a person who is speeding on his way to work has probabilities of 0.2, 0.1, 0.5, and 0.2 respectively, of passing through these locations, what is the probability that he will receive a speeding ticket?

b. If the person received a speeding ticket on his way to work, what is the probability that he was speeding when he passed through the radar trap at L2?

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