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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