Respuesta :
Answer:
The correct answer is D. 0.77
Step-by-step explanation:
[tex]X_i \text{ is the difference between true and reported age. where i = 1,2,3......48 }\\\text{The rounded age are uniformly distributed. So, }X_i = 0\\\\and,\thinspace O_{X_i}^2=\frac{\text{(Upper Bound - Lower Bound})^2}{5\times 2.5\text{ ( Rounded value )}}\\\\O_{X_i}^2=\frac{(2.5 + 2.5)^2}{12}\approx 2.083\\\\O_X_i=1.443[/tex]
[tex]\bar{X_{48}}=\frac{X_1+X_2+.......+X_{48}}{48}\\\\\bar{X_{48}}=\frac{\frac{48}{X_i}}{48}=0\\\\O_{\bar{X}_{48}}^2=\frac{48\cdot O_{X_i}^2}{48^2}=\frac{O_{X_i}^2}{48}\\\\\text{So, }\bar{X_i}\text{is approximately normal with mean 0 and standard deviation = }\\\\\frac{1.443}{\sqrt{48}}\approx 0.2083[/tex]
[tex]=Pr[\frac{-1}{4}\leq \bar{X}_{48}\leq \frac{1}{4}]\\\\=Pr[\frac{-0.25}{0.2083}\leq Z\leq \frac{0.25}{0.2083}]\\\\=Pr[-1.2\leq Z\leq 1.2]\\=Pr(Z\leq 1.2)-Pr(Z\leq -1.2)\\=Pr(Z\leq 1.2)-(1-Pr(Z\leq 1.2))\\=2\times 0.8849 -1\text{ ( Z value for 1.2 is 0.8849 )}\\\approx 0.77[/tex]
Hence, the correct answer is 0.77
