Question

1. The mean of a random sample of size 50 drawn from a population with mean 112 and standard deviation 40.

a. Find the sample mean.

b. Find the standard deviation of sample

c. What is the sample size?

d. What is the population mean?

e. If the population standard deviation is 40, compute for the variance population.

Answer 1

We are given that,

$n=50,\space \mu=112,\space \sigma=40$

a)

The sample mean given by $\mu_{\bar{x}}$ is $\mu_{\bar{x}}=\mu=112$

b)

The sample standard deviation given by $\sigma_{\bar{x}}$ is $\sigma_{\bar{x}}=\sigma/\sqrt{n}=40/\sqrt{50}=5.65685425$

Therefore, the sample standard deviation is, $\sigma_{\bar{x}}=5.65685425$

c)

The sample size $n=50$

d)

The population mean $\mu=112$.

e)

Given that the population standard deviation $\sigma=40,$ then the population variance is,

$\sigma^2=(\sigma)^2=40^2=1600$.

Therefore, the population variance is 1600.