Answer:
The probability of the sum of spins between 245 and 255 is 0.2534.
Explanation:
Let S = sum of 100 spins.
The expected value of the sum of 100 spins is, E (S) = 260.
The standard error of sum of 100 spins is, SE (S) = 12.
We need to compute the probability of the sum of spins between 245 and 255.
According to the Central Limit Theorem if we have a population with mean μ and standard deviation σ and we take appropriately huge random samples (n ≥ 30) from the population with replacement, then the distribution of the sum of values of X, i.e ∑X, will be approximately normally distributed.
Then, the mean of the distribution of the sum of values of X is given by,

And the standard deviation of the distribution of the sum of values of X is given by,

Compute the probability of the sum of spins between 245 and 255 as follows:
Apply continuity correction as follows:
P (245 ≤ S ≤ 255) = P (245 - 0.50 < S < 255 - 0.50)
= P (244.50 < S < 255.50)


*Use a z-table for the probability.
Thus, the probability of the sum of spins between 245 and 255 is 0.2534.