Question

A random sample of n=25 slides was taken; the time to board each flight was recorded. It was found that the mean amount of time to board the aircraft in the sample was x equals 42 minutes. Previous studies determined that boarding times were normally distributed with μ equals 38 minutes and a standard deviation of 36 minutes. The sample distribution of the sample mean x of size n equals 25 is ?

Answer 1

The sample distribution of the sample mean can be determined using the Central Limit Theorem. The mean of the sample mean is equal to the population mean, and the standard deviation of the sample mean is calculated by dividing the population standard deviation by the square root of the sample size.

Step-by-step explanation:

The sample distribution of the sample mean, x, of size n = 25 can be determined using the Central Limit Theorem. According to the Central Limit Theorem, when the sample size is large enough, the sample mean will be approximately normally distributed, regardless of the shape of the population distribution. In this case, the sample size is 25, which is considered large enough.

The mean of the sample mean, x, is equal to the population mean, μ. Therefore, the mean of the sample mean is 38 minutes.

The standard deviation of the sample mean is calculated by dividing the population standard deviation by the square root of the sample size. In this case, the population standard deviation is 36 minutes and the sample size is 25:

Standard Deviation of the Sample Mean = Population Standard Deviation / √(Sample Size)

Standard Deviation of the Sample Mean = 36 / √25 = 36 / 5 = 7.2 minutes

Therefore, the sample distribution of the sample mean, x, of size n = 25 has a mean of 38 minutes and a standard deviation of 7.2 minutes.