Question

The scores on a psychology exam were normally distributed with a mean of and a standard deviation of . About what percentage of scores were less than . The percentage of scores that were less than was

Answer 1

Complete Question

The scores on a psychology exam were normally distributed with a mean of 59 and a standard deviation of 6. About what percentage of sores were less than 53. The percentage of scores that were less than 53 was %. (Type an integer or a decimal.

Answer:

The value is
`P(X < 53) = 0.15866`

Explanation:

From the question we are told that

The mean is
`\mu = 59`

The standard deviation is
`\sigma = 6`

Generally the percentage that were less than 53 is mathematically represented as

`P(X < 53) = P((X - \mu )/(\sigma ) < ( 53 - 59 )/( 6 ) )`

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

=>
`P(X < 53) = P(Z < -1 )`

Generally the probability of (Z < -1 ) is

`P(Z < -1 ) = 0.15866`

=>
`P(X < 53) = 0.15866`