Question

An particular model of smartphone was advertised to have a battery life of 12 hours. The...

An particular model of smartphone was advertised to have a battery life of 12 hours. The manufacturer claims that the battery life for this model actually follows a Normal distribution with a mean of 11.63 hours and a standard deviation of 2.7 hours.

In a simple random sample of 11 phone of this model, the probability that the average battery life is less than 12 hours is:

Math   Statistics-And-Probability   
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Answer #1

Let X be the  battery life for for any given phone of this model. X has normal distribution with mean and standard deviation

Let be the average battery life of a randomly selected sample of n=11 phones. Since we know the population standard deviation of the battery life, using the central limit theorem we can say that   is normally distributed with mean and standard deviation (also called the standard error of mean)

the probability that the average battery life is less than 12 hours is

ans: the probability that the average battery life is less than 12 hours is 0.6736

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