A group of students at a school takes a history test The dis

A group of students at a school takes a history test. The distribution is normal with a mean of 25, and a standard deviation of 4.

(a) Everyone who scores in the top 30% of the distribution gets a certificate. What is the lowest score someone can get and still earn a certificate?

(b) The top 5% of the scores get to compete in a statewide history contest. What is the lowest score someone can get and still go onto compete with the rest of the state?

Solution

a)

Let lowest score someone can get and still earn a certificate S.

Let z-score corresponding to S be Z.

P( z > Z ) = 0.3

From normal table

Z = 0.524

using definitation of Z = (S-mu)/sigma

0.524 = (S-25)/4

S = 25+0.524*4 = 27.096 or 28

b)

Let lowest score someone can get and still go onto compete with the rest of the state S.

Let z-score corresponding to S be Z.

P( z > Z ) = 0.05

From normal table

Z = 1.645

using definitation of Z = (S-mu)/sigma

1.645 = (S-25)/4

S = 25+1.645*4 = 31.58 or 32