Question

solve Problem 16 section a) (Page 245), According to the Nielsen Company, teenagers between the ages of 13 and 17 send an average of 3340 text messages per month or moe hn stand devation for the population is 660 texts per random sample of 900 teenagers from this 13-to-17 month. a). What is the probability that the average number of texts for than slx texts every waking hour, You plan to draw a that the standard on. your sample will be somewhere between 3300 and 34007 0.7624 0.0624 0.9624 0.5624 0.3624

Answer 1

Given, $\mu$ = 3340 , $\sigma$ = 660

using central limit theorem,

P($\bar{x}$ < x) = P( Z < x - $\mu$ / $\sigma$ / sqrt(n)

P(3300 < $\bar{x}$ < 3400) = P( $\bar{x}$ < 3400) - P( $\bar{x}$ < 3300)

= P( Z < 3400 - 3340 / 660 / sqrt(900) ) - P( Z < 3300 - 3340 / 660 / sqrt(900) )

= P( Z < 2.7273) - P (Z < -1.8182)

= 0.9968 - 0.0344

= 0.9624