the proportions of multiple samples of registered voters who vote are normally distributed, with a mean…
the proportions of multiple samples of registered voters who vote are normally distributed, with a mean proportion of 0.38 and a standard deviation of 0.0485. what is the probability that a sample chosen at random has a proportion of registered voters who vote between 0.37 and 0.39? use the portion of the standard normal table below to help answer the question.\n| z | probability |\n| ---- | ---- |\n| 0.00 | 0.5000 |\n| 0.04 | 0.5160 |\n| 0.21 | 0.5832 |\n| 0.37 | 0.6443 |\n| 0.38 | 0.6481 |\n| 0.39 | 0.6517 |\n| 1.00 | 0.8413 |\n2%\n17%\n58%\n65%
Answer
Explanation:
Step1: Calcular z - scores
Para $x_1 = 0.37$, $z_1=\frac{0.37 - 0.38}{0.0485}\approx - 0.21$. Para $x_2 = 0.39$, $z_2=\frac{0.39 - 0.38}{0.0485}\approx0.21$.
Step2: Buscar probabilidades en la tabla
La probabilidad correspondiente a $z = - 0.21$ es $1 - 0.5832=0.4168$ (por la simetría de la distribución normal). La probabilidad correspondiente a $z = 0.21$ es $0.5832$.
Step3: Calcular la probabilidad entre los dos valores
$P(0.37<X<0.39)=0.5832 - 0.4168 = 0.1664\approx17%$.
Answer:
17%