statistics normal distribution

Question

in a certain school distract in a large metropolitan area, the SAT scores over the past five years are normally distributed with a mean of 1454. furthermore, Q3 is 1662. what is P98 score for the population.

Answer 1

thank you for your question!

in order to find the value here you want to use the equation

x = u + z*o, where u is the mean, z is the z score that goes with the 98^th percentile, and o is the standard deviation

the only value that is not given to us directly in the question is the standard deviation, but we can find that using the Q3 value of 1662

1662 = 1454 + 0.6745 * o

o = 308.38

putting it all together then we have

x = 1454 + 2.054*308.38

x = 2087.37

so you would expect the score in the 98^th percentile to be about 2087