Question

Based on a smartphone​ survey, assume that 57​% of adults with smartphones use them in theaters. In a separate survey of 277 adults with​ smartphones, it is found that 154 use them in theaters. a. If the 57​% rate is​ correct, find the probability of getting 154 or fewer smartphone owners who use them in theaters. b. Is the result of 154 significantly​ low?

Answer 1

Mean = np = 277 * 0.57 = 157.89

Standard deviation = sqrt ( np(1-p))

= sqrt(277 * 0.57 * 0.43)

= 8.2397

a)

Using normal approximation,

P(X <= x) = P( Z < x+0.5 - mean / SD)

So,

P( X <= 154) = P( Z <= 154.5 - 157.89 / 8.2397)

= P( Z < -0.4114)

= 0.3404

b)

Since probability of getting 154 or fewer smartphone owners who use them in theaters is greater than 0.05,

154 is not significantly low.