Question

The scores on a standardized Stat test are normally distributed with a mean of 100 and standard deviation 9. Students scoring below 85 on the test must take a remedial math course.
a) What percentage of students has to take the remedial math course?
b) The top 10% of students will be placed in the Honors statistics class. What score must a student get on the
test in order to be placed in Honors statistics?

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Answer 1

Solution :

Given that ,

mean =   = 100

standard deviation = = 9   

P(X<85 ) = P[(X- ) / < (85-100) /9 ]

= P(z < -1.67)

Using z table

= 0.0475

probability=0.0475

(B)

Using standard normal table,

P(Z > z) = 10%

= 1 - P(Z < z) = 0.10

= P(Z < z ) = 1 - 0.10

= P(Z < z ) = 0.90

= P(Z < 1.28 ) = 0.90

z = 1.28 (using standard normal (Z) table )

Using z-score formula  

x = z * +

x= 1.28 *9+100

x= 111.52