Respuesta :
Given:
P = 55% = 0.55
n = 500
Let's find the probability the number of students who say yes, they do won a car is between 270 and 290.
Now, let's first find the mean:
[tex]\mu=np=500*0.55=275[/tex]Let's find the standard deviation:
[tex]\begin{gathered} \sigma=\sqrt{npq} \\ \\ =\sqrt{500*0.55*1-0.55} \\ \\ =\sqrt[]{500*0.55*0.45} \\ \\ =11.12 \end{gathered}[/tex]Now, to find the probability, apply the formula:
[tex]z=\frac{x-\mu}{\sigma}[/tex][tex]P(270\leq x\leq290)=\frac{270-275}{11.12}\leq x\leq\frac{290-275}{11.12}[/tex]Solving further, we have:
[tex]=−0.44964\leq x\leq1.34892[/tex]Where:
P(270 < x < 290) = P(290) - P(270)
Using the standard normal table, we have:
NORMSDIST(-0.44964) = 0.32649
NORMSDIST(1.34892) = 0.91132
Hence, we have:
P(270 ≤ x ≤ 290 = P(290) - P(2870) = 0.91132 - 0.32649 = 0.58483
Therefore, the probability the number of students who say they own a car is between 270 and 290 is 0.585
ANSWER:
0.585
