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:

.632

step-by-step explanation:

6 * 1/10 = 3/5

3*0.01 = 0.03

3/5 + 0.03 = .63

2*0.002 = .002

.63 + 0.002 = .632

answer: 1722

step-by-step explanation:

given: the mass of saturn=

the mass of mercury=

the number of times the mass of saturn is greater than the mass of mercury

hence, the mass of saturn is 1722 times greater than the mass of mercury.