Question

A Pew Research report indicated that in 2008, 48% of teenagers aged 12-17
played video games on their cell phone. A random sample of 150 teenagers is
drawn.
a) Find the sample proportion.

b) What is the standard error?

c) Draw the bell curve for the study.

d) Find the z-score for 50%.

e) Draw the region on the standard bell that more than 50% play video games on
their cell phone.

f) What is the probability that more than 50% play video games on their cell
phones?

g) Would it be unusual if the sample proportion who played video games on their
cell phone was less than 40%? (Define Unusual to be less than 10% )

Answer 1

Part a)

Sample proportion    = p = 0.48

Part b)

Standard error = = 0.040792

Part c)

Part d)

Standardizing the value
Z = ( X - µ ) / σ
Z = ( 0.5 - 0.48 ) / 0.040792
Z = 0.4903

Part e)

Part f)

X ~ N ( µ = 0.48 , σ = 0.040792 )
P ( X > 0.5 ) = 1 - P ( X < 0.5 )
Standardizing the value
Z = ( X - µ ) / σ
Z = ( 0.5 - 0.48 ) / 0.040792
Z = 0.4903
P ( ( X - µ ) / σ ) > ( 0.5 - 0.48 ) / 0.040792 )
P ( Z > 0.4903 )
P ( X > 0.5 ) = 1 - P ( Z < 0.4903 )
P ( X > 0.5 ) = 1 - 0.688
P ( X > 0.5 ) = 0.3120

Part g)

X ~ N ( µ = 0.48 , σ = 0.040792 )
P ( X < 0.4 )
Standardizing the value
Z = ( X - µ ) / σ
Z = ( 0.4 - 0.48 ) / 0.040792
Z = -1.9612
P ( ( X - µ ) / σ ) < ( 0.4 - 0.48 ) / 0.040792 )
P ( X < 0.4 ) = P ( Z < -1.9612 )
P ( X < 0.4 ) = 0.0249

Event would be unusual if pobability is less than 10% i.e < 0.10

0.0249 < 0.10, hence it is unusual.