Respuesta :
Answer:
The probability that the sample proportion is more than 0.35 believe movie trailers reveal too much is 0.1539.
Step-by-step explanation:
According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.
The mean of this sampling distribution of sample proportion is:
[tex]\mu_{\hat p}=p[/tex]
The standard deviation of this sampling distribution of sample proportion is:
[tex]\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}[/tex]
The information provided is:
p = 0.32
n = 250
Since the sample size is quite large, i.e. n = 250 > 30, the central limit theorem can be used to approximate the sampling distribution of sample proportion by a Normal distribution.
Compute the probability that the sample proportion is more than 0.35 believe movie trailers reveal too much as follows:
[tex]P(\hat p>0.35)=P(\frac{\hat p-\mu_{\hat p}}{\sigma_{\hat p}}>\frac{0.35-0.32}{\sqrt{\frac{0.32(1-0.32)}{250}}})[/tex]
[tex]=P(Z>1.02)\\=1-P(Z<1.02)\\=1-0.84614\\=0.15386\\\approx 0.1539[/tex]
Thus, the probability that the sample proportion is more than 0.35 believe movie trailers reveal too much is 0.1539.
