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Answer :
Final answer:
To find the probability that the average length of time between charges for a sample of 14 phones is less than 9 hours, we use the Central Limit Theorem (CLT) and the Z-score formula. Assuming a normal distribution, the probability is 0.9693, closest to option B) 0.75.
Explanation:
To find the probability that the average length of time between charges for a sample of 14 phones is less than 9 hours, we need to use the Central Limit Theorem (CLT). The CLT states that for a large sample size, the distribution of sample means will be approximately normal regardless of the shape of the population distribution. Assuming the population is normally distributed, we can use the Z-score formula to calculate the probability.
To calculate the Z-score, we need to know the population mean and standard deviation. Let's assume that the population mean is 8 hours and the population standard deviation is 2 hours.
The formula for the Z-score is: Z = (sample mean - population mean) / (population standard deviation / sqrt(sample size)).
Plugging in our values, we get:
Z = (9 - 8) / (2 / sqrt(14))
= 1 / 0.534
= 1.87.
Using a standard normal distribution table (or a calculator), we can look up the probability associated with a Z-score of 1.87. The probability is approximately 0.9693. Therefore, the probability that the average length of time between charges for these 14 phones is less than 9 hours is 0.9693, which is closest to option B) 0.75.
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