Question

# At a local high school, 5000 juniors and seniors recently took an aptitude test. The results...

At a local high school, 5000 juniors and seniors recently took an aptitude test. The results of the test were normally distributed with a Mean of 450 and a Standard Deviation of 50. Calculate the following: The percent of students to the nearest tenth that scored over 525 The number of students that scored more than 475. The probability of a student selected at random, having scored between 400 and 575.

Solution :

Given that ,

1) P(x > 525) = 1 - p( x< 525 )

=1- p P[(x - ) / < (525 - 450) / 50 ]

=1- P(z < 1.50)

= 1 - 0.9332

= 0.0668

percentage = 6.7%

2) P(x > 475) = 1 - p( x< 475 )

=1- p P[(x - ) / < (475 - 450) / 50 ]

=1- P(z < 0.50)

= 1 - 0.6915

= 0.3085

= 5000 * 0.3085 = 1542.5

= 1543 students.

3) P( 400 < x < 575 ) = P[(400 - 450)/ 50 ) < (x - ) /  < (575 - 450) / 50) ]

= P(-1.00 < z < 2.50)

= P(z < 2.50 ) - P(z < -1.00 )

Using z table,

= 0.9938 - 0.1587

= 0.8351

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