the mean of sat scores of a specific month is1000 with a standard deviation of 100. find the 90 percentiles . assume that the sat score is normal distributed
To find the 90th percentile of SAT scores, we can use the Z-score formula in conjunction with the standard normal distribution table.
The Z-score measures the number of standard deviations a particular value is from the mean. In this case, we need to find the Z-score corresponding to the 90th percentile, which represents the score that is greater than or equal to 90% of all scores.
1. First, let's convert the percentile to a Z-score using the standard normal distribution table. The Z-score formula is given by:
Z = (X - μ) / σ
Where:
X = Data value (unknown)
μ = Mean of the distribution (1000 in this case)
σ = Standard deviation of the distribution (100 in this case)
Plugging in the values:
90% = (X - 1000) / 100
2. Now, let's rearrange the formula to solve for X:
X - 1000 = 0.90 * 100
X - 1000 = 90
X = 90 + 1000
X = 1090
So, the SAT score that corresponds to the 90th percentile is 1090.