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The time a cell phone lasts until it needs to be recharged is normally distributed with a mean of 14 hours and a standard deviation of 3 hours.

a) You need your cell phone to work for 10 hours as you are going on a hike. What is the probability that the cell phone will not last the 10 hours necessary? (In other words, what percentage of cell phones last 10 hours or less before needing to be recharged?)

Answer :

To find the probability that a cell phone lasts 10 hours or less, we calculate the Z-score for 10 hours (given a mean of 14 hours and a standard deviation of 3 hours), which is approximately -1.33, and then look up this Z-score in the standard normal distribution table to get the probability percentage.

The question asks about the probability that a cell phone will last 10 hours or less before it needs to be recharged. Given that the battery life is normally distributed with a mean of 14 hours and a standard deviation of 3 hours, we can calculate this probability using the standard normal distribution (Z-score).

First, we find the Z-score for 10 hours using the formula:

Z = (X - \\mu) / \\sigma

Where X is 10 hours, \\mu (mu) is the mean (14 hours), and \\sigma (sigma) is the standard deviation (3 hours).

Calculating the Z-score, we get:

Z = (10 - 14) / 3 = -4/3 \u2248 -1.33

To find the probability that the cell phone lasts 10 hours or less, we look up the Z-score of -1.33 in the standard normal distribution table (or use a calculator or software). This will give us the probability (as a percentage) that the cell phone will not last more than 10 hours. Normally distributed variables, Z-score, probability, and standard deviation are important concepts in this calculation.

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