Adult IQ scores have a bell-shaped distribution with mean of 100 and a standard deviation of 15. Use the Empirical rule to find the percentage of adults with scores between 70 and 130

Adult IQ scores have a bell-shaped distribution with mean of 100 and a standard deviation of 15. Use the Empirical rule to find the percentage of adults with scores between 70 and 130

 

answer:

The empirical rule applies to bell shaped, normal curve which states that,

1. About 68% of all values fall within 1 standard deviation of mean

2. About 95% of all values fall within 2 standard deviation of mean

3. About 99.7% of all values fall within 3 standard deviation of mean

So,

a. 100-70 = 30, which is twice the SDi.e( 2*15 = 30)

b. 100-130 = -30, which is twice the SD i.e( 2*15 = 30)

Hence, percentage of adults with scores 70 and 130 is 95%, which falls in 2 SD

for 250 students selected randomly,

85, is 100 -85 =15, which is 1 SD, i.e, 34% . So 250*34%=85 students have scored 85

130, is 100-130 = – 30, which is 2 SD, i.e, -47.5%. So 250*47.5% = 118.75 studens have scored 130

between 85 to 130, we have 85+118.75=203.75= 204

 

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