Question

Tyrell's SAT math score was in the 64th percentile. If all SAT math scores are normally distributed with a mean of 500 and a standard deviation of 100, what is Tyrell's math score? Round your answer to the nearest whole number.

z	0.00	0.01	0.02	0.03	0.04	0.05	0.06	0.07	0.08	0.09
0.0	0.5000	0.5040	0.5080	0.5120	0.5160	0.5199	0.5239	0.5279	0.5319	0.5359
0.1	0.5398	0.5438	0.5478	0.5517	0.5557	0.5596	0.5636	0.5675	0.5714	0.5753
0.2	0.5793	0.5832	0.5871	0.5910	0.5948	0.5987	0.6026	0.6064	0.6103	0.6141
0.3	0.6179	0.6217	0.6255	0.6293	0.6331	0.6368	0.6406	0.6443	0.6480	0.6517

Answer 1

Given that,

mean = = 500

standard deviation = = 100

Using standard normal table,

P(Z < z) = 64%

= P(Z < z) = 0.64

= P(Z <0.36 ) = 0.64

z = 0.36 ( Using standard normal z table,)

Using z-score formula  

x= z * +

x= 0.36 * 100+500

x= 536