Question

The state test scores for 12 randomly selected high school seniors are shown on the right. Complete parts​ (a) through​ (c) below. Assume the population is normally distributed. 1422 1222 985 693 729 840 723 746 542 620 1450 941

Answer 1

Solution:-

a) The sample mean is 909.417.

b) The sample standard deviation is 257.714.

$\sigma_{\bar{x}} = \sqrt{\frac{\sum \left ( x-\mu \right )^{2}}{(n-1)}}$

$\sigma_{\bar{x}} = \sqrt{\frac{730581.06944}{(12-1)}}$

$\sigma_{\bar{x}} = 257.714$

c) 95% confidence interval for the population mean is C.I = ( 763.602, 1055.232).

$C.I = \bar{x}\pm z_{\alpha /2}\ast \frac{\sigma }{\sqrt{n}}$

C.I = 909.417 + 1.96*74.3956

C.I = 909.417 + 145.8154

C.I = ( 763.602, 1055.232)