Question

Scores on a college entrance examination are normally distributed with a mean of 500 and a standard deviation of 100. What percent of people who write this exam obtain scores between 350 and 650?

Answer 1

The percentage is
`P(350 < X 650 ) = 86.6\%`

Explanation:

From the question we are told that

The population mean is
`\mu = 500`

The standard deviation is
`\sigma = 100`

The percent of people who write this exam obtain scores between 350 and 650

`P(350 < X 650 ) = P(( 350 - 500)/( 100) <( X - \mu )/( \sigma ) < (650 - 500)/( 100) )`

Generally

`(X - \mu )/(\sigma ) = Z (The \ standardized \ value \ of \ X )`

`P(350 < X 650 ) = P(( 350 - 500)/( 100) <Z < (650 - 500)/( 100) )`

`P(350 < X 650 ) = P(-1.5<Z < 1.5 )`

`P(350 < X 650 ) = P(Z < 1.5) - P(Z < -1.5)`

From the z-table
`P(Z < -1.5 ) = 0.066807`

and
`P(Z < 1.5 ) = 0.93319`

=>
`P(350 < X 650 ) = 0.93319 - 0.066807`

=>
`P(350 < X 650 ) = 0.866`

Therefore the percentage is
`P(350 < X 650 ) = 86.6\%`