Question

Based on a smartphone​ survey, assume that 41​% of adults with smartphones use them in theaters. In a separate survey of 264 adults with​ smartphones, it is found that 105 use them in theaters. a. If the 41​% rate is​ correct, find the probability of getting 105 or fewer smartphone owners who use them in theaters. b. Is the result of 105 significantly​ low?

Answer 1

Based on a smartphone​ survey, assume that 41​% of adults with smartphones use them in theaters. In a separate survey of 264 adults with​ smartphones, it is found that 105 use them in theaters.

If the 41​% rate is​ correct, find the probability of getting 105 or fewer smartphone owners who use them in theaters.

n=264, p=0.41

normal approximation to binomial used.

Expectation = np = 108.24

Variance = np(1 - p) = 63.8616

Standard deviation = 7.9913

With continuity correction , z value for 105, z =(105.5-108.24)/7.9913 = -0.34

P( x ≤105) = P(z < -0.34)

=0.3669

b. Is the result of 105 significantly​ low?

Since P( x ≤105) =0.3669 which is > 0.05, the result of 105 is not significantly​ low.