burban Families Watched An Average Of μ = 60 Minutes Of Television Each Day. Assuming That The Distribution Of Television-watching Times Is Normal With A Standard Deviation Of σ = 25 Minutes, Find Each Of The Following Proportions. A. What Proportion Of 2-year-old Children Watch ...This problem has been solved!See the answerA recent report indicates that 2-year-old children from well-educated suburban families watched an average of μ = 60 minutes of television each day. Assuming that the distribution of television-watching times is normal with a standard deviation of σ = 25 minutes, find each of the following proportions.a. What proportion of 2-year-old children watch more than 2 hours of television each day?b. What proportion of 2-year-old children watch less than 30 minutes a day?

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Asked Nov 28, 2019
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burban Families Watched An Average Of μ = 60 Minutes Of Television Each Day. Assuming That The Distribution Of Television-watching Times Is Normal With A Standard Deviation Of σ = 25 Minutes, Find Each Of The Following Proportions. A. What Proportion Of 2-year-old Children Watch ...

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A recent report indicates that 2-year-old children from well-educated suburban families watched an average of μ = 60 minutes of television each day. Assuming that the distribution of television-watching times is normal with a standard deviation of σ = 25 minutes, find each of the following proportions.

a. What proportion of 2-year-old children watch more than 2 hours of television each day?

b. What proportion of 2-year-old children watch less than 30 minutes a day?

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Expert Answer

Step 1

Given data

Mean µ = 60 min

Standard deviation σ = 25 minutes

a) proportion of 2-year-old children watch more than 2 hours(=120 minutes) of television each day is given by

P(X>120)

Changing into standard normal variate

P(X>120)
Changing into standard normal variate
120 60
120
P
(an0-2-210-)-
P(z> 2.4)
= Pz >
>
P(z > 2.4) 1 - P(z < 2.4)
1 - 0.9918 = 0.0082
(P(z 2.4) 0.9918(From Excel
= NORM. S. DIST(2.4, TRUE))
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Image Transcriptionclose

P(X>120) Changing into standard normal variate 120 60 120 P (an0-2-210-)- P(z> 2.4) = Pz > > P(z > 2.4) 1 - P(z < 2.4) 1 - 0.9918 = 0.0082 (P(z 2.4) 0.9918(From Excel = NORM. S. DIST(2.4, TRUE))

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Step 2

b) proportion of 2-year-old children watch less than 30 minutes a day is giv...

30 H
30 60
= Pz<
Р
<
25
P(Z 1.2) 0.115(From Excel
NORM. S. DIST(-1.2, TRUE))
help_outline

Image Transcriptionclose

30 H 30 60 = Pz< Р < 25 P(Z 1.2) 0.115(From Excel NORM. S. DIST(-1.2, TRUE))

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