Mathematics: The test results for a class with 24 students are normally distributed with a mean of 82 and a standard deviation of 8.9. What is the probability that a randomly chosen student earned a B or higher on the test (score of 80 or higher)?

+ 7Step-by-step explanation:...

The test results for a class with 24 students are

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14.02.2022

The value is P( X 80 ) = 0.58901

Step-by-step explanation:

From the question we are told that

The sample size is n = 24

The mean is $\mu = 82$

The standard deviation is $\sigma = 8.9$

Generally the probability that a randomly chosen student earned a B or higher on the test (score of 80 or higher ) is mathematically represented as

$P( X 80 ) = P( \frac{ X - \mu }{\sigma } \frac{ 80 - 82 }{ 8.9 } )$

$\frac{X -\mu}{\sigma } = Z (The \ standardized \ value\ of \ X )$

=> P( X 80 ) = P(Z -0.225 )

From the z table the area under the normal curve to the right corresponding to -0.225 is

P(Z -0.225 ) = 0.58901

=> P( X 80 ) = 0.58901

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