To solve this problem, we will use the concept of Z-score in statistics. The Z-score is a measure of how many standard deviations an element is from the mean.

Step 1: Identify the given values.
The population mean (μ) = 947
The standard deviation (σ) = 205
The sample size (n) = 60
The sample mean (x̄) = 900

Step 2: Calculate the standard error of the mean (σx̄). The standard error of the mean is the standard deviation of the sampling distribution of the mean. It is calculated as:

σx̄ = σ/√n = 205/√60 ≈ 26.46

Step 3: Calculate the Z-score. The Z-score is calculated as:

Z = (x̄ - μ) / σx̄ = (900 - 947) / 26.46 ≈ -1.78 (rounded to 2 decimal places)

Step 4: Look up the Z-score in the Z-table to find the probability. The Z-table tells us what percentage of the population is below (to the left of) our score.

Looking up a Z-score of -1.78 in the Z-table gives us a probability of 0.0375.

So, the probability that the mean score of a random sample of 60 students is below 900 is 0.0375 or 3.75% (rounded to 4 decimal places).

Question

To solve this problem, we will use the concept of Z-score in statistics. The Z-score is a measure of how many standard deviations an element is from the mean.

Step 1: Identify the given values.
The population mean (μ) = 947
The standard deviation (σ) = 205
The sample size (n) = 60
The sample mean (x̄) = 900

Step 2: Calculate the standard error of the mean (σx̄). The standard error of the mean is the standard deviation of the sampling distribution of the mean. It is calculated as:

σx̄ = σ/√n = 205/√60 ≈ 26.46

Step 3: Calculate the Z-score. The Z-score is calculated as:

Z = (x̄ - μ) / σx̄ = (900 - 947) / 26.46 ≈ -1.78 (rounded to 2 decimal places)

Step 4: Look up the Z-score in the Z-table to find the probability. The Z-table tells us what percentage of the population is below (to the left of) our score.

Looking up a Z-score of -1.78 in the Z-table gives us a probability of 0.0375.

So, the probability that the mean score of a random sample of 60 students is below 900 is 0.0375 or 3.75% (rounded to 4 decimal places).

Knowee AI · Accepted Answer

To solve this problem, we will use the concept of Z-score in statistics. The Z-score is a measure of how many standard deviations an element is from the mean.

Step 1: Identify the given values.
The population mean (μ) = 947
The standard deviation (σ) = 205
The sample size (n) = 60
The sample mean (x̄) = 900

Step 2: Calculate the standard error of the mean (σx̄). The standard error of the mean is the standard deviation of the sampling distribution of the mean. It is calculated as:

σx̄ = σ/√n = 205/√60 ≈ 26.46

Step 3: Calculate the Z-score. The Z-score is calculated as:

Z = (x̄ - μ) / σx̄ = (900 - 947) / 26.46 ≈ -1.78 (rounded to 2 decimal places)

Step 4: Look up the Z-score in the Z-table to find the probability. The Z-table tells us what percentage of the population is below (to the left of) our score.

Looking up a Z-score of -1.78 in the Z-table gives us a probability of 0.0375.

So, the probability that the mean score of a random sample of 60 students is below 900 is 0.0375 or 3.75% (rounded to 4 decimal places).

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