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If I take a sample of 14 phones, what is the probability that the average length of time between charges for these phones is less than 9 hours?

Answer :

The probability that the average length of time between charges for the sample of 14 phones is less than 9 hours is approximately 0.0307, or about 3.07%.

Here, we have to calculate the probability that the average length of time between charges for a sample of 14 phones is less than 9 hours, we can use the Central Limit Theorem.

The Central Limit Theorem states that the sampling distribution of the sample mean approaches a normal distribution as the sample size increases, regardless of the distribution of the population, as long as the sample size is sufficiently large.

Given that the average length of time between charges for a phone follows a certain distribution (which is not specified in the question), we'll assume that the distribution has a mean (μ) and a standard deviation (σ). For a sample size of 14, we can use the following formula to calculate the mean (μₛₐₘₚₗₑ) and standard deviation (σₛₐₘₚₗₑ) of the sample mean:

μₛₐₘₚₗₑ = μ (same as the population mean)

σₛₐₘₚₗₑ = σ / √n (n is the sample size)

In your question, you haven't provided the population mean (μ) or standard deviation (σ), so I'll assume hypothetical values for illustration purposes.

Let's say μ = 10 hours (population mean) and σ = 2 hours (population standard deviation), and n = 14 (sample size).

Now, calculate the mean and standard deviation of the sample mean:

μₛₐₘₚₗₑ = μ = 10 hours

σₛₐₘₚₗₑ = σ / √n = 2 / √14 ≈ 0.534

Now we want to find the probability that the average length of time between charges is less than 9 hours.

This can be calculated using the standard normal distribution (z-score):

z = (X - μₛₐₘₚₗₑ) / σₛₐₘₚₗₑ

z = (9 - 10) / 0.534 ≈ -1.87

Now, look up the corresponding cumulative probability (z-score) in a standard normal distribution table or use a calculator.

For a z-score of -1.87, the cumulative probability is approximately 0.0307.

So, the probability that the average length of time between charges for the sample of 14 phones is less than 9 hours is approximately 0.0307, or about 3.07%.

Read more about probability.

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