Suppose we choose independently 25 numbers at random (uniform density) from the interval [0, 20]. Write the normal densities that approximate the densities of their sum S25

Step-by-step explanation:

a=0 and b=20 in the uniform density function

∴ the mean μ===10 and

the variance ==.

The standard deviation is the square root of the variance, so

Having determined the mean and standard deviation of the uniform distribution, we can conclude that follows a normal distribution with and .

The normal probability distribution is:

So, substituting and

Having approximated sum , we move on to the standardized sum , which is the same as only with μ=0 and σ=1. This means the probability distribution is the standard normal distribution, which is:

70

step-by-step explanation:

step-by-step explanation: