According to an article on CNET.com (cnet.com/news/iphone-us-market-share-hit-lo

Question

According to an article on CNET.com (cnet.com/news/iphone-us-market-share-hit-low-point-prior-to-iphone-6s-launch/), the market share for theiPhone was 28.4% in August 2015. A recent consumer survey of 1000 randomly selected smartphone users found that 290 of them used an iPhone as their primary mobile device. If the market share is the same as it was in August 2015, what is the probability of getting 290 or more people in a sample of 1000 indicating that they use an iPhone? Round your answer to four decimal places. Hint: this problem uses the sampling distribution of the sample proportion.

Explanation / Answer

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value = 290/1000 =   0.29      
u = mean = p =    0.284      
          
s = standard deviation = sqrt(p(1-p)/n) =    0.014259874      
          
Thus,          
          
z = (x - u) / s =    0.420761088      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   0.420761088   ) =    0.336964774 [ANSWER]

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