Question

2. An investment company is planning upgrades to its website. The company believes 36% of its customers access the website through a smartphone. a) If the company takes a random sample of 200 recent visitors to the website, and checks the IP address to see if access was through a smartphone, give the properties (and provide a sketch) for the sampling ample proporti smartphone b) Find the probability the sample will yield less than 30% having accessed the website from a smartphone.

Answer 1

2)a) n = 200

       p = 0.36

$\mu_{\widehat p}$ = p = 0.36

$\sigma_{\widehat p}$ = sqrt(p(1 - p)/n)

      = sqrt(0.36 * (1 - 0.36)/200)

     = 0.0339

b) P( $\widehat p$ < 0.3)

= P(( $\widehat p$ - $\mu_{\widehat p}$ )/ $\sigma_{\widehat p}$ < (0.3 - $\mu_{\widehat p}$ )/ $\sigma_{\widehat p}$ )

= P(Z < (0.3 - 0.36)/0.0339)

= P(Z < -1.77)

= 0.0384