Question

Movie trailers are designed to attract large audiences. However. according to a recent survey, 32°A of Americans believe movie trailers give away too many of a movie’s best scenes, that is, they reveal too much. Suppose 250 Americans are selected at random and asKed if they believe movie trailers reveal too much. Find the probability that the sample proportion is more than 0.35.

Answer 1

The probability that the sample proportion is more than 0.35 believe movie trailers reveal too much is 0.1539.

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:

`\mu_(\hat p)=p`

The standard deviation of this sampling distribution of sample proportion is:

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

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:

`P(\hat p>0.35)=P((\hat p-\mu_(\hat p))/(\sigma_(\hat p))>\frac{0.35-0.32}{\sqrt{(0.32(1-0.32))/(250)}})`

`=P(Z>1.02)\\=1-P(Z<1.02)\\=1-0.84614\\=0.15386\\\approx 0.1539`

Thus, the probability that the sample proportion is more than 0.35 believe movie trailers reveal too much is 0.1539.