The proportion of combined gre scores can be expected to be between 155 and 160 is 0.1574
The mean of gre score = 150
The Standard deviation = 8.8
The proportion of combined gre score expected to be between 155 and 160 can be found using the normal distribution,
P(155 < x < 160)
Let us first find their standard score using the formula,
Z = (X -μ) / σ
where Z is the standard score
X is the random sample
μ is the mean
σ is the standard deviation
For x = 155,
Z = 155 - 150 / 8.8
= 5 / 8.8
= 0.57
For x = 160,
Z = 160 - 150 / 8.8
= 10/8.8
= 1.14
P(155 < x <160) = P( 0.54 < z < 1.14)
By using the z-table , we could find the value of P(0.54 < z < 1.14 ) will be 0.1574.
Therefore , the combined gre score between 155 and 160 is 0.1574.
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