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.**

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