A well-known mobile device company is preparing to launch a new model of cellphone within a specific range. The company is interested in defining certain technical specifications, also taking into account the variability of some aspects. A key aspect of the new cellphone is the charging time when using a standard charger. Specifically, testing was conducted on a large number of units of the new model, varying certain conditions like temperature and the condition of the cellphone. From this analysis, it was found that the charging time for a unit of this cellphone model, starting from 0% charge until reaching full charge, behaves as a random variable X with a Normal Distribution with a mean μ = 85 minutes and a standard deviation σ = 9 minutes. Based on the description above, solve the following questions: a. What is the probability that the charging time of a randomly selected cellphone will exceed 92 minutes? b. What is the probability that the charging time of a randomly selected cellphone will fall between 68 and 97 minutes? c. Suppose a random sample of 42 cellphones is selected from the random variable X. Calculate the expected number of cellphones for which the charging time will be between 68 and 97 minutes. Interpret the result. Help: To solve this question, it is useful to think in two steps. In the first, calculate the probability of the event in one unit, and in the second, consider the number of trials to calculate the requested expected value.
A well-known mobile device company is preparing to launch a new model of cellphone within a specific range. The company is interested in defining certain technical specifications, also taking into account the variability of some aspects. A key aspect of the new cellphone is the charging time when using a standard charger. Specifically, testing was conducted on a large number of units of the new model, varying certain conditions like temperature and the condition of the cellphone. From this analysis, it was found that the charging time for a unit of this cellphone model, starting from 0% charge until reaching full charge, behaves as a random variable X with a Normal Distribution with a mean μ = 85 minutes and a standard deviation σ = 9 minutes. Based on the description above, solve the following questions: a. What is the probability that the charging time of a randomly selected cellphone will exceed 92 minutes? b. What is the probability that the charging time of a randomly selected cellphone will fall between 68 and 97 minutes? c. Suppose a random sample of 42 cellphones is selected from the random variable X. Calculate the expected number of cellphones for which the charging time will be between 68 and 97 minutes. Interpret the result. Help: To solve this question, it is useful to think in two steps. In the first, calculate the probability of the event in one unit, and in the second, consider the number of trials to calculate the requested expected value.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:A well-known mobile device company is preparing to launch a new model of cellphone within a
specific range. The company is interested in defining certain technical specifications, also taking into
account the variability of some aspects. A key aspect of the new cellphone is the charging time when
using a standard charger. Specifically, testing was conducted on a large number of units of the new
model, varying certain conditions like temperature and the condition of the cellphone. From this
analysis, it was found that the charging time for a unit of this cellphone model, starting from 0%
charge until reaching full charge, behaves as a random variable X with a Normal Distribution with a
mean μ = 85 minutes and a standard deviation σ = 9 minutes.
Based on the description above, solve the following questions:
a. What is the probability that the charging time of a randomly selected cellphone will exceed 92
minutes?
b. What is the probability that the charging time of a randomly selected cellphone will fall between
68 and 97 minutes?
c. Suppose a random sample of 42 cellphones is selected from the random variable X. Calculate the
expected number of cellphones for which the charging time will be between 68 and 97 minutes.
Interpret the result.
Help: To solve this question, it is useful to think in two steps. In the first, calculate the probability of the
event in one unit, and in the second, consider the number of trials to calculate the requested expected
value.
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