Let P be the proportion of americans who support the death penalty is which is 0.53.
P follows Normal distribution with parameters
mean = p=0.53
standard deviation = [tex] \sqrt{\frac{p*(1-p)}{n}} [/tex]
= [tex] \sqrt{\frac{0.53*(1-0.53)}{1000}} [/tex]
standard deviation = 0.0157
The probability that the sample proportion of those supporting the death penalty will be less than 0.50
P(P < 0.50) = [tex] P( \frac{P-mean}{standard deviation} < \frac{0.50 - 0.53}{0.0157} ) [/tex]
= P(Z < -1.91)
P(P < 0.50)= 0.0281
The probability that the sample proportion of those supporting the death penalty will be less than 0.50 is 0.0281
