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 [tex]P(X < 53) = 0.15866[/tex]
Step-by-step explanation:
From the question we are told that
The mean is [tex]\mu = 59[/tex]
The standard deviation is [tex]\sigma = 6[/tex]
Generally the percentage that were less than 53 is mathematically represented as
[tex]P(X < 53) = P(\frac{X - \mu }{\sigma } < \frac{ 53 - 59 }{ 6 } )[/tex]
[tex]\frac{X -\mu}{\sigma } = Z (The \ standardized \ value\ of \ X )[/tex]
=> [tex]P(X < 53) = P(Z < -1 )[/tex]
Generally the probability of (Z < -1 ) is
[tex]P(Z < -1 ) = 0.15866[/tex]
=> [tex]P(X < 53) = 0.15866[/tex]
