Answer to Question #345727 in Statistics and Probability for Etheral

Question

2000 Grade 11 students of DNHS took a Statistics test. The scores were distributed normally with a mean of 70 and Standard deviation of 10. Label the mean and three standard deviation from the mean.

1. What percentage of scores are between 70 and 80?

2. What percentage of scores are between 60 and 80?

3. What percentage of scores less than a score of 60?

Answer 1

$\mu=70, \sigma=10, 3\sigma=30$

1.

$$P(70<X<80)$$

$$=P(Z<\dfrac{80-70}{10})-P(Z\le\dfrac{70-70}{10})$$

$$=P(Z<1)-P(Z\le0)$$

$$=0.8413-0.5=0.3413$$

$34.13\%$

2.

$$P(60<X<80)$$

$$=P(Z<\dfrac{80-70}{10})-P(Z\le\dfrac{60-70}{10})$$

$$=P(Z<1)-P(Z\le-1)$$

$$=0.84134-0.15866=0.6827$$

$68.27\%$

3.

$$P(X<60)=P(Z<\dfrac{60-70}{10})$$

$$=P(Z<-1)=0.1587$$

$15.87\%$