Question

If scores are normally distributed with a mean of 30 and a standard deviation of 5.what percentage of the scores is?

Answer 1

If scores are normally distributed with a mean of 30 and a standard deviation of 5, what percent of the scores is:

(a) greater than 30?

(b) greater than 37?

 (c) between 28 and 34?

(a)

$$P(X>30)=1-P(Z\le\dfrac{30-30}{5})=0.5$$

50%

(b)

$$P(X>37)=1-P(Z\le\dfrac{37-30}{5})$$

$$=1-P(Z\le1.4)\approx0.080757$$

8.0757%

(c)

$$P(28<X<34)=P(Z<\dfrac{34-30}{5})$$

$$-P(Z\le\dfrac{28-30}{5})=P(Z<0.8)-P(Z\le-0.4)$$

$$\approx0.7881446-0.3445783\approx0.443566$$

44.3566%