91影视

Referring to exercise 4.173 (p. 282), the study discovers that the application was downloaded by 40% of adults on their cell phones. The percentage applied to the population of adult cell phone owners.

So, the probability$p=0.40$

a.

Consider the standard error of the 50 random sample,$蟽$

So,

$\begin{array}{rcl}蟽& =& \sqrt{\frac{p\left(1-p\right)}{n}}\\ & =& \sqrt{\frac{0.40脳0.60}{50}}\\ & =& 0.692\\ & & \end{array}$

Now, the probability that more than 60% have downloaded the application is,

$\begin{array}{rcl}\mathrm{Pr}\left(X>0.60\right)& =& \mathrm{Pr}\left(\frac{\hat{p}-p}{蟽}>\frac{0.60-0.40}{0.692}\right)\\ & =& \mathrm{Pr}\left(z>2.89\right)\\ & =& 1-\mathrm{Pr}\left(z<2.89\right)\\ & =& 1-0.99807\\ & =& 0.0020\\ & & \end{array}$

Therefore, there is a very low chance of 0.2% that more than 60% have downloaded the application.

b.

Referring to part a., the sample proportion is too small. So, there can assume that either the sample is taken randomly or there is a problem in the population mean proportion.

c.

Hence the sample is from the International Association for the Wireless Telecommunication industry. So, the sample is biased and categorizes the adults from the same industry who are more interested to download the application.

Therefore, the population mean can鈥檛 be rejected and there is no problem with that. So, the sample is taken randomly.