Answer to Question #269176 in Statistics and Probability for Melody balbalosa

Question

A certain experiment conducted was normally distributed. The mean value is 50 and the standard deviation is 4. If the total population is 1000 (discrete variable), calculate the percentage of the population within z=-1.4 and z=2.56

Answer 1

Here, $\mu=50,\space \sigma =4 \space, N=1000$

To find the percentage of the population within z=-1.4 and z=2.56, we first determine the probability that the population is within z=-1.4 and z=2.56. This probability is given as,

$p(-1.4\leqslant Z\leqslant 2.56)=\phi(2.56)-\phi(-1.4)$ which is obtained from the normal tables as,

$\phi(2.56)-\phi(-1.4)=0.9948-0.0808=0.9140$

To find the percentage of the population within this interval, we express the probability found above in percentage form by multiplying by 100%.

The probability in percentage is, 0.9140*100%=91.4%

Therefore, the percentage of the population within z=-1.4 and z=2.56 is 91.4%.