Answer to Question #305635 in Statistics and Probability for Camilala

Question

A random variable has a moral distribution with mean of 60 and standard deviation 4. Find the percent data with each interval

a. Between 60 and 70

b. Between 53 and 60

c. Between 54 and 71

d. Greater than 65

c. Less than 62.48

Answer 1

a.

$$P(60<X<70)=P(X<70)-P(X\le60)$$

$$=P(Z<\dfrac{70-60}{4})-P(Z\le\dfrac{60-60}{4})$$

$$=P(Z<2.5)-P(Z\le0)$$

$$\approx0.9938-0.5=0.4938$$

b.

$$P(53<X<60)=P(X<60)-P(X\le53)$$

$$=P(Z<\dfrac{60-60}{4})-P(Z\le\dfrac{53-60}{4})$$

$$=P(Z<0)-P(Z\le-1.75)$$

$$\approx0.5-0.04006=0.4599$$

c.

$$P(54<X<71)=P(X<71)-P(X\le54)$$

$$=P(Z<\dfrac{71-60}{4})-P(Z\le\dfrac{54-60}{4})$$

$$=P(Z<2.75)-P(Z\le-1.5)$$

$$\approx0.99702-0.06681=0.9302$$

d.

$$P(X>65)=1-P(X\le65)$$

$$=1-P(Z\le\dfrac{65-60}{4})$$

$$=1-P(Z\le1.25)$$

$$\approx0.10565$$

e.

$$P(X<62.48)=P(Z<\dfrac{62.48-60}{4})$$

$$=P(Z<0.62)\approx0.73237$$