Given that on one section of the SAT the mean is 500 and the standard deviation is 100, what is the approximate probability of a student scoring 600 or higher on the test? Round as appropriate.
post answer
To find the approximate probability of a student scoring 600 or higher on the SAT test, we need to use the standard normal distribution.
Step 1: Convert the raw score (600) to a z-score using the formula:
z = (x - μ) / σ
where x is the raw score, μ is the mean, and σ is the standard deviation.
Plugging in the values given:
z = (600 - 500) / 100
z = 1
Step 2: Look up the z-score in the standard normal distribution table or use a calculator to find the area under the curve to the left of the z-score.
Using a standard normal distribution table, the area to the left of z = 1 is approximately 0.8413.
Step 3: Subtract the area obtained from 1 to find the area to the right of the z-score.
1 - 0.8413 = 0.1587
Step 4: Round the result to the appropriate number of decimal places.
Rounding 0.1587 to three decimal places, the approximate probability of a student scoring 600 or higher on the SAT test is 0.159.
To find the approximate probability of a student scoring 600 or higher on the test, we need to use the concept of standard scores, also known as z-scores.
A z-score measures the number of standard deviations a particular value is from the mean. It helps us understand how an individual score compares to the overall distribution.
To calculate the z-score for a given value, we can use the formula:
z = (x - μ) / σ
where:
- z is the z-score
- x is the value we want to find the z-score for
- μ is the mean
- σ is the standard deviation
In this case:
- x = 600
- μ = 500
- σ = 100
Substituting the values into the formula:
z = (600 - 500) / 100
z = 1
Now, we need to find the probability associated with a z-score of 1. We can refer to a standard normal distribution table or use a calculator with a standard normal distribution function.
Using a standard normal distribution table, we can find the z-score of 1.00, which corresponds to a probability of approximately 0.8413. This represents the probability up to the z-score of 1.
However, we are interested in the probability of scoring 600 or higher. To obtain this probability, we subtract the probability up to the z-score of 1 from 1 (since the total probability is 1).
P(z > 1) = 1 - P(z < 1)
= 1 - 0.8413
= 0.1587 (rounded to four decimal places)
Therefore, the approximate probability of a student scoring 600 or higher on the SAT test is approximately 0.1587, or 15.87% when rounded to the nearest percent.
Z = ( score - mean )/SD = (600-500)/100 = ?
Look up Z score in table in the back of your statistics text to get the probability.