Answer to Question #343920 in Statistics and Probability for Rookie

Question

1. In a population of high school students algebra scores the mean 64 and the standard deviation of 6. Find the z values that corresponds to a score x = 81
2. A geometry score is 40. If it is given than mean is 42 and the standard deviation is 7.What is the corresponding z score
3. The average credit card debt for public school teacher is 14975. if the debut is normally distributed with a standard deviation of 5,650 find the probabilities

a. That the teacher owes at least 6,740

b. that the teacher owes more than 19270

c. that the teacher owes between 6740 and 19270

Answer 1

1.

$$z=\dfrac{x-\mu}{\sigma}=\dfrac{81-64}{6}=\dfrac{17}{6}\approx2.833 3$$

2.

$$z=\dfrac{x-\mu}{\sigma}=\dfrac{40-42}{7}=-\dfrac{2}{7}\approx-0.2857 3$$

3.

a.

$$P(X\ge6740)=1-P(Z<\dfrac{6740-14975}{5650})$$

$$\approx1-P(Z<-1.4575)\approx0.9275$$

b.

$$P(X>19270)=1-P(Z\le\dfrac{19270-14975}{5650})$$

$$\approx1-P(Z\le0.7602)\approx0.2236$$

c.

$$P(6740<X<19270)=P(Z<\dfrac{19270-14975}{5650})$$

$$-P(Z\le\dfrac{6740-14975}{5650})\approx P(Z<0.7602)$$

$$-P(Z\le-1.4575)\approx0.77643-0.07249$$

$$\approx0.7039$$