* i need answer question 94 93 Test scores. Many states assess the skills of the

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* i need answer question 94

93 Test scores. Many states assess the skills of their students in various grades. One program that is available for this purpose is the National Assessment of Educational Progress (NAEP). One of the tests provided by the NAEP assesses the reading skills of 12th-grade students. In a re- cent year, the national mean score was 288 and the standard deviation was 38. Assuming that these scores are approximately Normally distrib- uted, N(288, 38), use the 68-95-99.7 rule to give a range of scores that includes 95% of these students. Use the 68-95-99.7 rule. Refer to the previous exercise. Use the 68-95- 997 rule to give a range of scores that includes 99.7% of these students. 94

Explanation / Answer

According to the emperical rule :-

Within 1 standard deviation of the mean on both sides refers to 68% of the data

Within 2 standard deviation of the mean on both sides refers to 95% of the data

Within 3 standard deviation of the mean on both sides refers to 99.7% of the data

So,

For 99.7% of population, standard deviation should be equal to 3 from the mean on either side of the mean.

Lower Range = Mean - (3* Standard Deviation)

= 288 - (3*38)

= 288 - 114

= 174

Similarly,

Upper Range = Mean + (3* Standard Deviation)

= 288 + (3*38)

= 288 + 114

= 402

Therefore, there are 99.7% of the students in between the scores of 174 and 402.

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