Question

Assume critical reading scores for a standardized test are distributed as

​N(470​, 50​) Complete parts​ (a) through​ (d) below. (Round A, B and C to the nearest Integer as needed)

A. Find the test score at the 75th percentile. The 75th percentile is _____.

B. Find the Test score at the 25th percentile The 25th percentile is _____.

C. Find the interquatile range for test scores. Th e Interquartile range is _______.

D. Is the Interquartile range is larger or smaller than the standard deviation? ________(Pick either smaller or larger)

Answer 1

A) P(X < x) = 0.75

Or, P((X - )/ < (x - )/ ) = 0.75

Or, P(Z < (x - 470)/50) = 0.75

Or, (x - 470)/50 = 0.67

Or, x = 0.67 * 50 + 470

Or, x = 503.5

B) P(X < x) = 0.25

Or, P((X - )/ < (x - )/ ) = 0.25

Or, P(Z < (x - 470)/50) = 0.25

Or, (x - 470)/50 = -0.67

Or, x = -0.67 * 50 + 470

Or, x = 436.5

C) IQR = Q3 - Q1

= 503.5 - 436.5

= 67

D) The interquartile range is larger than the standard deviation.