Question

The reading speed of sixth-grade students is approximately normal with a mean speed of 125 words per minute and a standard deviation of 24 words per minute.

(Note: Labelled diagrams and proper notation are required for all parts.)

e) What is the reading speed for a sixth-grader who can read faster than 90% of all sixth-graders?

f) A school psychologist wants to determine unusually fast reading rates and unusually slow

reading rates. Determine the reading rates of the middle 95% of all sixth-graders. What are the cutoff points for unusual readers?

Answer 1

u = 125, = 24

we have,

z = (x-u)/

e) What is the reading speed for a sixth-grader who can read faster than 90% of all sixth-graders?

Thus, probability = 0.90

Corresponding z score = 1.28

Thus,

1.28 = (x-125)/24

Thus, x = 125 + 1.28*24

= 155.72 words per minute

f) A school psychologist wants to determine unusually fast reading rates and unusually slow reading rates. Determine the reading rates of the middle 95% of all sixth-graders. What are the cutoff points for unusual readers?

=> According to the Empirical rule, approximately 95% of observation will fall within two standard deviations of the mean

Thus, confidence interval

= (u-2* to u+2*)

= (125-2*24 to 125+2*24)

= (77, 173)

Cutoff points for unusual readers are points which are more than 3 standard deviations away from mean

i,e less than (125-3*24) or greater than (125+3*24)

i.e. less than (53) or greater than (197)