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

Answer 1

Answer:

$P(x < 535.8) = 0.64$

$P_{64} = 535.8$

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 500

Standard Deviation, σ = 100

We are given that the distribution of SAT score is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

We have to find the value of x such that the probability is 0.64

P(X<x) = 0.64

$P( X < x) = P( z < \displaystyle\frac{x - 500}{10})=0.64$  

Calculation the value from standard normal z table, we have,  $p(z<0.358) = 0.64$

$\displaystyle\frac{x - 500}{100} = 0.358\\x = 535.8$

$P(x < 535.8) = 0.64$

$P_{64} = 535.8$