Question

# The average verbal GRE score is 400 with a standard deviation of 100. Based on this...

The average verbal GRE score is 400 with a standard deviation of 100. Based on this information, answer questions a-c

(a) What verbal GRE score will put a person in the BOTTOM 53% ?

(b) Using the same mean verbal GRE score and standard deviation, if 36 students took the GRE, how many people would be expected to have verbal GRE scores ABOVE 350? Round to the nearest person.

(c) Graduate school A requires students to have a verbal GRE score of 540 to be accepted into the program. If a person is picked at random from the distribution of ALL GRE scores, what is the chance that the student would have the required GRE score or higher to be accepted to Graduate School A?

a)

X ~ N ( µ = 400 , σ = 100 )
P ( X < x ) = 53% = 0.53
To find the value of x
Looking for the probability 0.53 in standard normal table to calculate Z score = 0.0753
Z = ( X - µ ) / σ
0.0753 = ( X - 400 ) / 100
X = 407.53

b)

X ~ N ( µ = 400 , σ = 100 )
P ( X > 350 ) = 1 - P ( X < 350 )
Standardizing the value
Z = ( X - µ ) / σ
Z = ( 350 - 400 ) / 100
Z = -0.5
P ( ( X - µ ) / σ ) > ( 350 - 400 ) / 100 )
P ( Z > -0.5 )
P ( X > 350 ) = 1 - P ( Z < -0.5 )
P ( X > 350 ) = 1 - 0.3085
P ( X > 350 ) = 0.6915

Of the 36 students we expect 36 * 0.6915 = 24.89 = 25

c)

X ~ N ( µ = 400 , σ = 100 )
P ( X > 540 ) = 1 - P ( X < 540 )
Standardizing the value
Z = ( X - µ ) / σ
Z = ( 540 - 400 ) / 100
Z = 1.4
P ( ( X - µ ) / σ ) > ( 540 - 400 ) / 100 )
P ( Z > 1.4 )
P ( X > 540 ) = 1 - P ( Z < 1.4 )
P ( X > 540 ) = 1 - 0.9192
P ( X > 540 ) = 0.0808

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