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The Bank of America trends in Consumer Mobility Report indicates that in a typical day, 51% of users of mobile phones use their phone at least once per hour, 26% use their phone a few times per day, 8% use their phone morning and evening, and 13% hardly ever use their phones. The remaining 2% indicated that they did not know how often they used their mobile phone ( USA today, July 7, 2014). Consider a sample of 150 mobile phone users. a. What is the probability that at least 70 use their phone at least once per hour? b. What is the probability that at least 75 but less than 80 use their phone at least once per hour? c. What is the probability that less than 5 of the 150 phone users do not know how often they use their phone?

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STATISTICS F/BUSINESS+ECONOMICS-TE...

13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884
BuyFind

STATISTICS F/BUSINESS+ECONOMICS-TE...

13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884

Solutions

Chapter
Section
Chapter 6.3, Problem 31E
Textbook Problem
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The Bank of America trends in Consumer Mobility Report indicates that in a typical day, 51% of users of mobile phones use their phone at least once per hour, 26% use their phone a few times per day, 8% use their phone morning and evening, and 13% hardly ever use their phones. The remaining 2% indicated that they did not know how often they used their mobile phone (USA today, July 7, 2014). Consider a sample of 150 mobile phone users.

  1. a. What is the probability that at least 70 use their phone at least once per hour?
  2. b. What is the probability that at least 75 but less than 80 use their phone at least once per hour?
  3. c. What is the probability that less than 5 of the 150 phone users do not know how often they use their phone?

Expert Solution

a.

To determine

Find the probability that at least 70 use phone at least once per hour.

Explanation of Solution

Calculation:

In report of bank of America trends in consumer mobility, the 51% of mobile users use their phone at least once per hour, 26% use their phone a few times a day, 8% use their phone morning and evening in a day and 13% use hardly ever their phones. The 2% users did not know how often they use their phone.

The formula for mean in binomial distribution is,

μ=np

The value of mean is,

μ=150×0.51=76.5

The formula for standard deviation is,

σ=np(1p)

The value of standard deviation is,

σ=150×0.51(10.51)=150×(0.51×0.49)=37.485=6.1225

Continuity correction:

The binomial probability is converted to a normal probability by using the continuity correction.

If the binomial probability represents “fewer than c” then the normal probability is P(x<c0

Expert Solution

b.

To determine

Find the probability of at least 75 but less than 80 users are in the category at least once per hour.

Expert Solution

c.

To determine

Find the probability of less than 5 users do not know how often they use their phone.

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Chapter 6 Solutions

STATISTICS F/BUSINESS+ECONOMICS-TEXT
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