in 120 throws of a six faced die the even numbers occur 55times.is this die Unbiased?
Answers
Answer:
Yes, this die unbiased..
Given : in 120 throws of a six faced die the even numbers occur 55times
To find : Is this die Unbiased
Solution:
Normal Dice will have 60 throws of even number
p = 60/120 = 1/2
q = 1 - 1/2 = 1/2
n = 120
mean = np = 60
variance = npq = 60 * (1/2) = 30
variance = SD²
SD = √30 = 5.477
Z score = ( Value - Mean)/SD
for 95 % confidence interval
60 ± 1.96 * 5.477
=> 49.26 to 70.74
55 lies in between
Die is unbiased
for 99 % confidence interval
60 + 2.575 * 5.477
=> 46 to 64
55 lies in between
Die is unbiased
for 90% confidence interval
60 + 1.645 * 5.477
=> 51 to 69
55 lies in between
Die is unbiased
Die is unbiased
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