Question

Based on a smartphone​ survey, assume that 45​% of adults with smartphones use them in theaters. In a separate survey of 203 adults with​ smartphones, it is found that 78 use them in theaters. a. If the 45​% rate is​ correct, find the probability of getting 78 or fewer smartphone owners who use them in theaters. b. Is the result of 78 significantly​ low? a. If the 45​% rate is​ correct, the probability of getting 78 or fewer smartphone owners who use them in theaters is

Answer 1

Solution:-
Given proportion of adults using smartphones in theatres = p = 0.45.

The total adults with smart phones in survey = n = 203.

The total number of adults used smartphone = 78

proportion of adults used smartphones = x/n = 78/203 = 0.3842

P(X <= 78) = P(p^ <= 0.3842)
=> P((p^-p)/sqrt(pq/n) < (0.3842-0.45)/sqrt(0.45*0.55/203)))
= P(Z < -1.8844)
= 1 - P(Z < 1.8844)
= 1 - 0.9699
= 0.0301

  
b. The probability is mall and thus the result is significantly low.