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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

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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 ) &nbsp;= &nbsp;Z (The &nbsp;\ standardized \ &nbsp;value\ &nbsp;of &nbsp;\ X )

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

Generally the probability of (Z < -1 ) is


P(Z < -1 ) = 0.15866

=>
P(X < 53) = 0.15866

User Muhammad Tarique
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