Question

1. A basketball player makes 54% of his shots during the regular season games.
a) To simulate whether a shot hits or misses you could assign random digits as
follows:
(i) One digit simulates one shot; 1 and 5 are a make, other digits are a miss.
(ii) One digit simulates one shot; odd digits are a make and even digits are a miss.
(iii) Two digits simulate one shot; 00 to 54 are a make and 55 to 99 are a miss.
(iv) Two digits simulate one shot; 00 to 53 are a make and 54 to 99 are a miss.
(v) Two digits simulate one shot; 01 to 54 are a make and 55 to 99 are a miss.

b) Using your choice in part (a) and these random digits below, simulate 10 shots.
12734 75390 20867 27513

c) Compute estimated probability:

Answer 1

True probability = p =0.54

(i) One digit simulates one shot; 1 and 5 are a make, other digits are a miss.

Simulated random digits: 12734 75390

Among this 2 are make (bold ones) out of 10.

So estimated probability = .

(ii) One digit simulates one shot; odd digits are a make and even digits are a miss.

Simulated random digits: 1 2 7 3 4 7 5 3 9 0

Among this 7 are make (bold and underlined ones) out of 10.

So estimated probability = .

(iii) Two digits simulate one shot; 00 to 54 are a make and 55 to 99 are a miss.

Simulated random digits: 12 73 47 53 90 20 86 72 75 13

Among this 5 are make (bold and underlined ones) out of 10.

So estimated probability = .

(iv) Two digits simulate one shot; 00 to 53 are a make and 54 to 99 are a miss.

Simulated random digits: 12 73 47 53 90 20 86 72 75 13

Among this 4 are make (bold and underlined ones) out of 10.

So estimated probability = .

(iii) Two digits simulate one shot; 01 to 54 are a make and 55 to 99 are a miss.

Simulated random digits: 12 73 47 53 90 20 86 72 75 13

Among this 5 are make (bold and underlined ones) out of 10.

So estimated probability = .