Question

Please provide answers for a and b, Thank You :)

Based on a smartphone​ survey, assume that 50​% of adults with smartphones use them in theaters. In a separate survey of 271 adults with​ smartphones, it is found that 134 use them in theaters.

a. If the 50​% rate is​ correct, find the probability of getting 134 or fewer smartphone owners who use them in theaters.

b. Is the result of 134 significantly​ low?

Answer 1

a) Let X denotes the number of smartphone owners who use them in theaters out of 271 adults with​ smartphones.

X ~ Binomial(271, p)

If the 50​% rate is​ correct, then we can assume p = 0.5

So, X ~ Binomial(271, 0.5)

The probability mass function of X is

The probability of getting 134 or fewer smartphone owners who use them in theaters

b) The probability of getting 134 smartphone owners who use them in theaters

Since P(X = 134) is quite significant from 0,so the result of 134 is not significantly​ low.