Question

A random number generator returns random floats between 0 and 1, according to a uniform distribution. say you let the random number generator draw 100 numbers, the sample mean will be...

A.impossible to determine, because the data aren't drawn from a normal distribution. B.normally distributed, with mean 0.5 and standard deviation 0.2887.

C.uniformely distributed, between 0 and 1. D.normally distributed, with mean 0.5 and standard deviation 0.02887.

Answer 1

According to given statement a random number generates returns random floats between 0 and 1. It means that a random variable is uniformly distributed over 0 and 1. Now 100 samples have drawn of this random variable to see the distribution of sample mean.

We know in case of normal distribution sampling distribution follow normal distribution. In other words we know that according to central limit theorem if sample size increases then sampling distribution from the population which has normal distribution approximately close to normal distribution.

But in case of uniform distribution, on increasing sample size , sampling distribution does not confirm normal distribution.

in sampling distribution from uniform distribution there will be lake of uniformity . Sampling distribution maybe right skewed or left skewed in case when parent population is uniformly distributed. It means that sampling distribution does not follow normal distribution or uniform distribution. we cannot determine its distribution.

Hence option A is correct.