Question

1. SAT scores were originally scaled so that the scores for each section were approximately normally distributed with a mean of 500 and a standard deviation of 100.

Assuming that this scaling still applies, use a table of standard normal curve areas to find the probability that a randomly selected SAT student scores
a. More than 700.
b. Between 440 and 560.

Answer 1

a) 0.02275

b) 0.4515

Explanation:

Data provided in the question:

Mean = 500

Standard deviation, s = 100

Now,

a) More than 700

z score = [ X - mean ] ÷ s

= [700 - 500 ] ÷ 100

= 2

P(More than 700) = P(z > 2 )

or

P(More than 700) = 0.02275 [ from standard z vs P table ]

b) Between 440 and 560

z score for X = 440

= [440 - 500 ] ÷ 100

= - 0.6

z score for X = 560

= [560 - 500 ] ÷ 100

= 0.6

Now,

P( Between 440 and 560 ) = P (z < 0.6 ) - P( z < -0.6 )

thus,

P( Between 440 and 560 ) = 0.7257469 - 0.2742531

= 0.4515