Mathematics: [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.

37 is the right answer because 47 is not mutable and 27 is too short ...

[9] X is a Gaussian random variable with variance - id909777999, angieinthehouse45

samueltaye

13.02.2022

The minimum number of samples required is n = 16641

Step-by-step explanation:

From the question we are told that

The variance is $\sigma^2 = 0.25$

The margin of error is E = 0.01

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

$\alpha = (1 - 0.99 ) \%$

=> $\alpha = 0.01$

Generally from the normal distribution table the critical value of $\frac{\alpha }{2}$ is

$Z_{\frac{\alpha }{2} } = 2.58$

Generally the standard deviation is

$\sigma =\sqrt{\sigma^2}$

=> $\sigma =\sqrt{0.25}$

=> $\sigma =0.5$

Generally the sample size is mathematically represented as

$n = [\frac{Z_{\frac{\alpha }{2} } * \sigma }{E} ] ^2$

=> $n = [\frac{2.58 } * 0.5 }{0.01 } ] ^2$

=> n = 16641

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