[9] X is a Gaussian random variable with variance 0.25. The mean of X is estimated by taking the sample mean of independent samples of X. If the mean needs to be estimated within 0.01 from the actual mean with a confidence coefficient of 0.99, find the minimum number of samples needed in the estimation.

The minimum number of samples required is    

Step-by-step explanation:

From the question we are told that

    The variance is  

    The margin of error is

From the question we are told the confidence coefficient is  0.99 , hence the level of significance is    

=>  

Generally from the normal distribution table the critical value  of   is  

Generally the standard deviation is

=>  

=>  

Generally the sample size is mathematically represented as  

=>      

=>              

2 equivalent expressions to represent the area of a rectangle and the top is n-3 and the side is 2

area of the rectangle = length * width

given length = n - 3

width = 2

replace it in the area

so area of the rectangle = (n-3) *2

= 2(n-3)

one of the expression is 2(n-3)

to get another expression we distribute 2 inside the parenthesis

2(n-3) is 2n - 6

so another expression is 2n - 6

two equivalent expression are

2(n - 3)   , 2n - 6