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  • In a statistics class, the mean and standard deviation of the scores obtained by students on a test were found to be 61 and 10, respectively. If the scores are normally distributed, what percentage

In a statistics class, the mean and standard deviation of the scores obtained by students on a test were found to be 61 and 10, respectively. If the scores are normally distributed, what percentage of students scored below 65?

 

Option: 1

52.33%


Option: 2

96.25%


Option: 3

65.52%


Option: 4

86.77%


Answers (1)

best_answer

To determine the percentage of students who scored below 65, we can use the properties of a normal distribution. Given that the mean (\mu) is 61 and the standard deviation (\sigma) is 10, we can calculate the z-score corresponding to a score of 65 and then find the percentage of scores below that z-score.

The z-score is calculated using the formula:

\mathrm{z=(x-\mu) / \sigma}

Where:
\mathrm{x} is the individual score
\mathrm{\mu} is the mean
\mathrm{\sigma} is the standard deviation

In this case, we want to find the z-score for \mathrm{x= 65}:

\mathrm{\begin{aligned} & z=(65-61) / 10 \\ & z=0.4 \end{aligned}}

Once we have the z-score, we can look up the corresponding percentage in the standard normal distribution table or use a calculator that provides this functionality. From the table, we find that the percentage of scores below a z-score of 0.4 is approximately 65.52%.

Therefore, approximately 65.52% of students scored below 65.

 

Posted by

manish painkra

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