Question

The scores of the students on a standardized test are normally distributed, with a mean of 500 and a standard deviation of 110. What is the probability that a randomly selected student has a score between 350 and 550

Answer 1

The probability that a randomly selected student has a score between 350 and 550 = 0.5867

Explanation:

Mean
`(\\u )` = 500

Standard deviation
`(\sigma )` = 110

Let X be the score of student in a standardized test

The probability that a randomly selected student has a score between 350 and 550 =

`P(350< X< 550)` =
`P(( 350 - 500 )/(110 )< ( X - \\u )/(\sigma )< ( 550 - 500 )/(110 ) )`

=
`P(- 1.36< Z< 0.45 )` Putting
`(Z =( X - \\u )/(\sigma ))`

=
`(Z< 0.45) - (Z< -1.36)`

= 0.6736 - .0869 ( Using Z table )

= 0.5867