Question

Suppose Students’ scores on the SAT are normally distributed with μ= 1509 and σ= 321

A) What percentage of a students score less than 1188? (An approximate answer is fine here)

B) What percentage of a students score between 867 and 2151? (An approximate answer is fine here)

C) Find the probability of a student scoring more than 1600

Answer 1

Given data,

μ= 1509 and σ= 321

A)

P(X < 1188)

= P( X-μ / σ < 1188 - 1509 / 321)

= P( Z < -1) [ From z-table]

= 0.1587

B)

P(867 < X < 2151)

= P( 867-1509 / 321 < X-μ / σ < 2151 - 1509 / 321)

= P( -2 < Z < 2)

= P( Z < 2) -P( Z < -2) [ From z-table]

= 0.9772 - 0.0228

= 0.9544

C)

P(X > 1600 )

= P( X-μ / σ > 1600- 1509 / 321)

= 1 - P( Z < 0.28)  [ From z-table]

= 1 - 0.6103

= 0.3897

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