Question

A reading specialist wants to identify third-graders who scored at the lowest 10% on a standardized reading test in elementary school A so she can offer additional assistance to the students. What is the probability of randomly picking a third grader from this school and the child having a reading score at the lowest 10%?

School A has 240 third-graders. How many third-graders will meet the criterion of scoring at the bottom 10% on the standardized reading test?

The raw scores on the standardized reading test are normally distributed so the raw scores can be converted into a distribution of Z scores. If we want to mark the lower 10% of the distribution on the Z distribution, what is the Z value that is the cut-off point for that 10% tail region? (Answer with the exact Z value found from the Z table)

What would be the cut-off raw score if we want to mark the bottom 10% on the distribution of raw scores? The population mean of the reading scores is 100 and the standard deviation is 10. (Round the answer to two decimal places)

Luke and Austin are both third-graders in School A and they scored 80 and 90, respectively. Will they fall into the lowest 10% to receive additional assistance from the reading specialist?

Answer #1

>> Out of 100 % students 10 % fall at the bottom

probability of third-grader and having a reading score at the lowest 10% = 10 / 100 = 0.1

>> 240 third graders

bottom 10% = 10% of 240 = 24

>> As the scores is assumed to be normally distributed

Prob( z <=x ) = 0.1

( here we need to find x so looking at the standard normal table and searching x for which Prob( z <=x ) = 0.1 )

x = - 2.33

>> Given mean( u ) =100 and sd =10

Z = ( X - u ) / sd

- 2.33 = ( X - 100 ) / 10

X = 76.70

>> As both Luke and Austin score above the cutoff value of 76.70 so both of them didnt fall under the bottom 10 %

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