A fair die is tossed 1620 times

G

Guest

Guest
A fair die is tossed 1620 times.

a. What is the mean number of 4's expected?
b. What is the standard deviation of the distribution of 4's?
c. Between what two numbers would you expect the number of 4's to fall 95% of the time?
 
G'day,

The probability of a dice throw landing on a four is 1/6. That is \(\displaystyle \pi\).

For a and b, check out the similar post of yours I replied to.

For c, apply a normal distribution approximation. The area under the curve between the mean and the higher number is 0.95/2=0.475.

The corresponding Z-score is 1.96. Apply the formula Z = (X - mu)/sigma, using the mean and SD you calculated in and b. Use the symmetry of the curve to find the lower number.

Note that you need to round the higher number down and the lower number up if they are decimals to ensure the discrete region is not extended.
 
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