Question

The proportion of americans who support the death penalty is 0.53. a sample of 1000 randomly selected americans is surveyed by telephone interview. the probability that the sample proportion of those supporting the death penalty will be less than 0.50 is

Answer 1

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 =
`\sqrt{(p*(1-p))/(n)}`

=
`\sqrt{(0.53*(1-0.53))/(1000)}`

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) =
`P( (P-mean)/(standard deviation) < (0.50 - 0.53)/(0.0157) )`

= 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