Samples are drawn from a population with mean 118 and standard deviation 36. Each sample
has 374 randomly and independently chosen elements.
Use the Central Limit Theorem to estimate the probability that a sample mean is less than
120.

To estimate the probability that a sample mean is less than 120 using the Central Limit Theorem, we can use the formula for the standard error of the mean:

Standard Error (SE) = standard deviation / sqrt(sample size)

SE = 36 / sqrt(374)

SE ≈ 1.857

Next, we calculate the z-score using the formula:

z = (sample mean - population mean) / SE

z = (120 - 118) / 1.857

z ≈ 1.077

Using a standard normal distribution table or a calculator, we can find the probability that a z-score is less than 1.077. This probability represents the likelihood that a sample mean is less than 120.

Samples are drawn from a population with mean 118 and standard deviation 36. Each samplehas 374 randomly and independently chosen elements.Use the Central Limit Theorem to estimate the probability that a sample mean is less than120.​

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Samples are drawn from a population with mean 118 and standard deviation 36. Each sample
has 374 randomly and independently chosen elements.
Use the Central Limit Theorem to estimate the probability that a sample mean is less than
120.