Question

Fill in the Blanks The National Center for Education Statistics reports that mean scores on the standardized math test for eighth-graders in 2009 increased slightly from those for previous years. The mean score in 2009 was 283. Assume that the standard deviation is 10. Find the probability that the test score of a randomly selected eighth-grader was greater than 290 What proportion of test scores was between 295 and 300? Suppose students who scored at the 5th percentile or lower could not graduate. Find the 5th percentile test score. Suppose you know someone who scored 258 on the test. Is this unusual? On what do you base your answer? (Say Yes or No or Moderately) and justify on the paper copy.

Answer 1

Given : Il - 28 3 ; solo ca) D G > 290) = 1 - Pas290) (x-4 210-283) E I - P -1- P(Z < 0.7) (from 2-table) C, ° (6) Pl 295<x< 300) = 61295-283 300 - 283 I 10 10 = P ( 1.2 <2 < 1,7) = P(Z < 1.7 - P(Z { 1.2) - 0.9554 - 0.8849_ (from 2 table = 0.0705 (c) To find sth such that normel table, z percentile first we have to find Z p(2 <Z)=0.05, from stand =-1-645 Now Z - X-ul X = u tzo x = 283 - 1.6458 lo x = 266.55 | (d) find 2-score of X = 258 -2.5 2= x - M - 258-283 io since 23-2.5 is below 2-standard deviation of the mean. Therefore someone who score 258 is unusual