Question

A normal die (numbered 1-6) is fair if each outcome is equally likely. Therefore a 1 should come up of the time. If a fair die is rolled 360 times we would expect a 1 to come up 60 times (since 1 over 6 times 360 equals 60 ). If x represents the number of times a "1" is rolled then open vertical bar fraction numerator x minus 60 over denominator square root of 50 end fraction close vertical bar less than 1.96 gives the reasonable range for the number of times a "1" will come up in 360 rolls. If we roll the die 360 times and get a "1" 30 times, is our die a fair die? Show your work using the equation editor.

Answer 1

Yes the die is fair as the calculated z= -0.224 is less than the Z∝= 1.96

Explanation:

x`- u / s/√n< Z∝

x`- 60 /√50/√360 < 1.96

From the above we find that u = 60 and the sample size n= 360 S= √ 50

Z∝= 1.96

Here p = 1/6 ( the probability of getting a 1 out of 6)

q= 5/6

Since it is normal Standard deviation = √npq = √360 * 1/6*5/6= √50

If x`= 30

then

30 - 60 /√50/√360 < 1.96

-30/7.07*18.973 < 1.96

- 0.224 < 1.96

Yes the die is fair as the calculated z= -0.224 is less than the Z∝= 1.96 the null hypothesis that die rolled is fair is accepted.