Aproduction company 350 hourly employes have 37.5 years of age with 8.3 of years standard deviation. If random sample of 45 it taken. Then what is the probability that the sample will have an average age less than or equal to 40?
We will use the central limit theorem to calculate the probability.
First, we need to calculate the mean and standard deviation of the sampling distribution of the sample means.
The mean of the sampling distribution is equal to the mean of the population, which is given as 37.5 years.
The standard deviation of the sampling distribution (also called the standard error) is equal to the standard deviation of the population divided by the square root of the sample size.
standard error = standard deviation / sqrt(sample size)
standard error = 8.3 / sqrt(45)
standard error = 1.236
Next, we need to standardize the sample mean using Z-score formula.
Z = (sample mean - population mean) / standard error
Z = (40 - 37.5) / 1.236
Z = 2.02
Finally, we need to find the probability of getting a Z-score less than or equal to 2.02. We can use a standard normal distribution table or calculator to find this probability.
Using a Z-table, we find that the probability of getting a Z-score less than or equal to 2.02 is approximately 0.9783.
Therefore, the probability that the sample will have an average age less than or equal to 40 is 0.9783 or 97.83%.
The largest mountan in ethiopia is?
The largest mountain in Ethiopia is Mount Ras Dashen, which has an elevation of 4,550 meters (14,928 feet).
To answer this question, we can use the Central Limit Theorem, which states that for a large enough sample size (usually greater than 30), the sampling distribution of the sample mean will be approximately normally distributed, regardless of the shape of the original population.
First, let's find the mean and standard deviation of the sampling distribution of the sample mean.
Mean of the sampling distribution (µx̄) = Mean of the population = 37.5
Standard deviation of the sampling distribution (σx̄) = Standard deviation of the population / √(sample size)
= 8.3 / √(45)
= 8.3 / 6.71
≈ 1.24
Now, we can calculate the probability that the sample will have an average age less than or equal to 40 using a z-score.
Z-score = (Sample mean - Population mean) / Standard deviation of the sampling distribution
= (40 - 37.5) / 1.24
≈ 2.02
Using a standard normal distribution table or a statistical calculator, we can find the cumulative probability associated with the z-score of 2.02.
The probability that the sample will have an average age less than or equal to 40 is approximately 0.9781, or 97.81%.
Note: In this calculation, we assumed that the population follows a normal distribution. If this assumption does not hold, the result may not be accurate.