A certain standardized​ test's math scores have a​ bell-shaped distribution with a mean of 525 and a standard deviation of .119 Complete parts​ (a) through​ (c).

Question

A certain standardized​ test's math scores have a​ bell-shaped distribution with a mean of

525

and a standard deviation of

119.

Complete parts​ (a) through​ (c).

Question content area bottom

Part 1

​(a) What percentage of standardized test scores is between

168

and

882​?

enter your response here​%

​(Round to one decimal place as​ needed.)

Part 2

​(b) What percentage of standardized test scores is less than

168

or greater than

882​?

enter your response here​%

​(Round to one decimal place as​ needed.)

Part 3

​(c) What percentage of standardized test scores is greater than

763​?

enter your response here​%

​(Round to one decimal place as​ needed.)

Answer 1

Part 1

a) P(168 < X < 882)

= P( (168-525)/119 < Z < (882-525)/119)

= P( -3 < Z < 3)

=P{ Z < 3 ) - P(Z < -3)

= 0.99865 - 0.00135

= 0.9973

99.7%

Part 2

b) P(X < 168 or X > 882)

= P (Z < -3 or Z > 3)

= P(Z < -3) + P(Z > 3 )

= 0.00135 + 0.00135

= 0.0027

Or it can be computed as 1 minus the answer to part !

1-0.9973 = 0.0027

0.3%

Part 3

c) P(X > 763)

= P( Z > (763-525)/119)

=P(Z > 2)

= 1- P(Z <2) = 1- 0.9972 = 0.0028

0.3%