High School

Most graduate schools of business require applicants for admission to take the Graduate Management Admission Council's GMAT examination. Scores on the GMAT are roughly normally distributed with a mean of 260 and a standard deviation of 38.

a) What is the probability of an individual scoring above 200 on the GMAT?

b) What is the probability that a randomly selected student's score will be less than 220?

c) What is the probability that a randomly selected student scores exactly 300?

Answer :

a) The probability of an individual scoring above 200 on GMAT is = 0.94283.

b) The probability that a randomly selected student score will be less than 220 = 0.14617.

c) The probability that a randomly selected student score exactly 300 is = 0.85374.

Scores on the GMAT are roughly normally distributed.

The mean of normal distribution = (μ) = 260.

Standard deviation of the distribution = (σ) = 38.

(a) when x = 200 then z score is,

z = (x - μ)/σ = (200 - 260)/38 = - 1.579 [Rounding off to third decimal places]

The probability of an individual scoring above 200 on GMAT is

= P(x ≥ 200)

= P(z ≥ - 1.579)

= 1 - P(z ≤ - 1.579)

= 1 - 0.057168

= 0.94283

(b) when x = 220 then z score is,

z = (220 - 260)/38 = -1.053 [Rounding off to third decimal places]

The probability that a randomly selected student score will be less than 220 is

= P(x ≤ 220)

= P(z ≤ -1.053)

= 0.14617

(c) when x = 300 then z score is,

z = (300 - 260)/38 = 1.053 [Rounding off to third decimal places]

The probability that a randomly selected student score exactly 300 is

= P(x = 300)

= P(z = 1.053)

= 0.85374

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