Question

#4 Approximately 78 percent of 18 to 24 year olds currently are using Snapchat. What is the probability that in a random sample of 8 people aged 18 to 24, at least 7 are using Snapchat?

#5 In 2014, 53 percent of millennial voters were Democrats. In a random sample of 200 millennial voters, what is the probability that more than 55% are democrats?

Answer 1

4)

X ~ Binomial (n,p)

Where n = 8 , p = 0.78

Binomial probability distribution is

P(X) = ⁿC_x p^x (1-p)^n-x

So,

P( X >= 7) = P( X= 7) + P( X = 8)

= ⁸C₇ 0.78⁷ 0.22 + ⁸C₈ 0.78⁸ 0.22⁰

= 0.4462

5)

Given,

p = 0.53 , n = 200

We have to calculate P( > 0.55) = ?

Using normal approximation  

P( < p ) = P( Z < - p / sqrt( p ( 1- p) / n) )

So,

P( > 0.55) = P( Z > 0.55 - 0.53 / sqrt( 0.53 * 0.47 / 200) )

= P( Z > 0.5667)

= 1 - P( Z < 0.5667)

= 1 - 0.7145

= 0.2855