1.) The RAND() function in Microsoft Excel generates a number that is supposed t

Question

1.) The RAND() function in Microsoft Excel generates a number that is supposed to be uniformly distributed between 0 and 1.0. What is the probability that the next number returned by this function will be greater than 0.60?____

2.)Continuing, what is the mean, or "expected value", of this random variable?

3.) Suppose we use this function repeatedly to produce 100 of these "pseudo-random" numbers. We then take the mean of these 100 values, which I'll call "M".

4.) What is the expected value of M?_____It turns out that the standard deviation of a single random variable that is uniformly distributed between 0 and 1 is 0.2887. What is the standard deviation of the mean of 100 independent values of this random variable?

5.)Continuing, the Central Limit Theorem tells us that, even though these variables are certainly not Normal random variables, the mean of a sufficiently large number of them will be. Use this to estimate the probability that M (this mean of 100 independent random numbers, each uniformly distributed between 0 and 1), will be between 0.45 and 0.55.

Explanation / Answer

1) as it is uniformly distributed P(X>0.6) =0.4

2)expected value =(0+1)/2 =0.5

4)expected value of mean =0.5

std deviation =0.2887/(100)1/2 =0.02887

5)P(0.45<X<0.55) =P((0.45-0.5)/0.02887<Z<(0.55-0.5)/0.02887)= P(-1.7319<Z<1.7319)=0.9584-0.0416 =0.9167

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