Respuesta :
Answer:
The probability that the sample proportion will be less than 0.11 = .9982
Step-by-step explanation:
Given -
Suppose the true proportion is 0.07 .
true proportion [tex](\nu _{\widehat{p}})[/tex] = p = 0.07
q = 1 - p = 1 - 0.07 = 0.93
n = 343
Standard deviation [tex](\sigma _{\widehat{p}})[/tex] = [tex]\sqrt{\frac{p\times q}{n}}[/tex] = [tex]\sqrt{\frac{0.07\times 0.93}{343}}[/tex] = .0137
the probability that the sample proportion will be less than 0.11 =
[tex]P(\widehat{p}< 0.11)[/tex] = [tex]P(\frac{\widehat{p} - \nu _{\widehat{p}}}{\sigma _{\widehat{p}}}<\frac{ 0.11 - 0.07}{.0137})[/tex] using[ [tex]z = \frac{\widehat{p} - \nu _{\widehat{p}}}{\sigma _{\widehat{p}}}[/tex]]
= [tex](z< 2.91)[/tex]
= .9982
