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Answer :
Final answer:
The LG phone lasts at least 8 hours about 95.25% of the time. The probability that it lasts less than 7 hours is almost 0, thus not likely. More than 11 hours would be unusual, and the top 10% of call times is at 9.77 hours.
Explanation:
This is a problem of normal distribution in Statistics. The first thing to note is that we have the mean (μ = 9 hours) and the standard deviation (σ = 0.6 hours) for the LG phone video call time.
1. To find the proportion of time that the phone will last at least 8 hours, we first need to find the Z score: Z = (X - μ) / σ = (8 - 9) / 0.6 = -1.67. Using a Z-table, the area to the left of -1.67 is about 0.0475, which means the LG phone will last at least 8 hours about 95.25% of the time (1 - 0.0475).
2. Similarly, to find the probability a fully charged phone will last less than 7 hours, calculate the Z-score: Z = (7 - 9) / 0.6 = -3.33. Looking at the Z-table, the value corresponding to -3.33 is almost 0, implying that the phone will almost never last less than 7 hours.
3. For the question whether it would be unusual for the LG phone to last more than 11 hours, calculate the Z-score: Z = (11 - 9) / 0.6 = 3.33. The corresponding value in the Z-table is almost 1, implying it's almost impossible hence, it would be unusual.
4. To find the call time represented by the top 10% of all video call times, we look for the Z-score that leaves 10% of the distribution to the right: this Z-score is +1.28. Solve for X: X = Zσ + μ = 1.28 * 0.6 + 9 = 9.77 hours.
Learn more about Normal Distribution here:
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