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.

1. Find the probability that the test score of a randomly selected eighth- grader was greater than 290

2. What proportion of test scores was between 295 and 300?

3. Suppose students who scored at the 5th percentile or lower could not graduate. Find the 5th percentile test score.

4. 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

Answer;

Given,

mean = 283

standard deviation = 10

a)

P(X > 290) = P((x-u)/s > (290 - 283)/10)

= P(z > 0.7)

= 0.2419637 [since from z table]

= 0.2420

b)

P(295 < X < 300) = P((295 - 283)/10 < (x-u)/s < (300 - 283)/10)

= P(1.2 < z < 1.7)

= P(z < 1.7) - P(z < 1.2)

= 0.9554345 - 0.8849303  [since from z table]

= 0.0705

c)

Given,

P(z < Z) = 0.05

since from standard normal table

z = - 1.645

Consider,

x = u + z*s

substitute values

= 283 - 1.645*10

= 283 - 16.45

= 266.55

d)

Here x = 258

consider,

z = (x - u)/s

substitute values

= (258 - 283)/10

= - 2.5

Here it is below 2 standard deviation of mean , so it is unusual.