The expected value of the sum of 100 spins is 280 points with a standard error of points. The probability that the sum of 100 spins will be between 245 and 255, inclusively, is approximately , using a Normal approximation with a continuity correction. (Answer to four decimal places.)

The probability of the sum of spins between 245 and 255 is 0.2534.

Step-by-step 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.

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7.25

step-by-step explanation:

we know that 7 equals to 7.0. we also know that 1/4=0.25. so we can add the two together and we get 7.25