# 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

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

Asked on May 18, 2017 in