Question

A poll agency reports that 75% of teenagers aged 12-17 own smartphones. A random sample of 234 teenagers is drawn. Round your answers to four decimal places as needed. Part 1. Find the mean . Part 2. out of 6 Find the standard deviation

Answer 1

Answer:

If our random variable of interest for this case is X="the number of teenagers between 12-17 with smartphone" we can model the variable with this distribution:

$X \sim Binom(n=234, p=0.75)$

And the mean for this case would be:

$E(X) =np = 234*0.75= 175.5$

And the standard deviation would be given by:

$\sigma =\sqrt{np(1-p)}= \sqrt{234*0.75*(1-0.75)}= 6.624$

Step-by-step explanation:

If our random variable of interest for this case is X="the number of teenagers between 12-17 with smartphone" we can model the variable with this distribution:

$X \sim Binom(n=234, p=0.75)$

And the mean for this case would be:

$E(X) =np = 234*0.75= 175.5$

And the standard deviation would be given by:

$\sigma =\sqrt{np(1-p)}= \sqrt{234*0.75*(1-0.75)}= 6.624$