SAT math test scores for all students taking the test are approximately normally distributed with mean score of 514 and std. deviation of 118.


What is the probability that a randomly chosen student will earn a score above 600 on their SAT math test?

There's 19 students, suppose that everyone in class will take the SAT math test soon. What is the probability that the mean score of the class will be above 600?

I just need the second question, I discovered the first answer iis 72.88%

Z = (score-mean)/SEm

SEm = SD/sqrt n

Use same table.

To find the probability that a randomly chosen student will earn a score above 600 on their SAT math test, we need to calculate the z-score and then use a z-table or a calculator to find the corresponding probability.

Step 1: Calculate the z-score using the formula:

z = (x - μ) / σ

where:
x = score (600 in this case)
μ = mean score (514)
σ = standard deviation (118)

z = (600 - 514) / 118
z = 0.728

Step 2: Use a z-table or a calculator to find the probability associated with the z-score of 0.728.

Looking up the z-score of 0.728 in a standard normal distribution table, we find that the probability is approximately 0.7669.

Therefore, the probability that a randomly chosen student will earn a score above 600 on their SAT math test is approximately 0.7669 or 76.69%.

Now, to calculate the probability that the mean score of the class will be above 600, we need to use the concept of the sampling distribution of the sample mean.

Step 1: Calculate the standard error of the sample mean (σm) using the formula:

σm = σ / sqrt(n)

where:
σ = standard deviation (118)
n = sample size (19)

σm = 118 / sqrt(19)
σm ≈ 27.06

Step 2: Calculate the z-score using the formula:

z = (x - μ) / σm

where:
x = score (600 in this case)
μ = mean score (514)
σm = standard error of the sample mean (27.06)

z = (600 - 514) / 27.06
z ≈ 3.18

Step 3: Use a z-table or a calculator to find the probability associated with the z-score of 3.18.

Looking up the z-score of 3.18 in a standard normal distribution table, we find that the probability is almost 1.

Therefore, the probability that the mean score of the class will be above 600 is approximately 1 or 100%.